Preamble sequence generation method in wireless LAN system

ABSTRACT

Disclosed is a sequence generation method for: generating a basic sequence structure comprising C 52 , which is composed of 52 tones, and D 12 , which is composed of 12 tones; selecting any one among a plurality of phase rotation factors, which are determined in advance for a bandwidth and applied to the basic sequence structure by unit of C 52  or C 52 D 12 ; and generating a sequence inserted into a preamble to be transmitted to a terminal.

TECHNICAL FIELD

The present invention relates to a wireless communication system, andmore particularly, to a method for generating a sequence forcommunication between a base station and a user equipment and apparatustherefore.

BACKGROUND ART

Recently, with development of information communication technology,various wireless communication technologies have been developed. Amongothers, a wireless local area network (WLAN) enables wireless access tothe Internet using a portable terminal such as a personal digitalassistant (PDA), a laptop, a portable multimedia player (PMP) in a home,an enterprise or a specific service provision area based on radiofrequency technology.

In order to overcome limitations in communication rate which have beenpointed out as weakness of a WLAN, in recent technical standards, asystem for increasing network speed and reliability and extendingwireless network distance has been introduced. For example, in IEEE802.11n, multiple input and multiple output (MIMO) technology usingmultiple antennas in a transmitter and a receiver has been introduced inorder to support high throughput (HT) with a maximum data rate of 540Mbps or more, to minimize transmission errors, and to optimize datarate.

As next-generation communication technology, machine-to-machine (M2M)communication technology has been discussed. Even in an IEEE 802.11 WLANsystem, technical standards supporting M2M communication have beendeveloped as IEEE 802.11ah. In M2M communication, a scenario in which asmall amount of data is communicated at a low rate may be considered inan environment in which many apparatuses are present.

Communication in a WLAN system is performed in a medium shared betweenall apparatuses. As in M2M communication, if the number of apparatusesis increased, in order to reduce unnecessary power consumption andinterference, a channel access mechanism needs to be more efficientlyimproved.

DISCLOSURE OF THE INVENTION Technical Task

An object of the present invention devised to solve the problem is toimprove performance of a sequence that will be transmitted to a userequipment in a new communication system.

Another object of the present invention is to maximize an AGC (AdaptiveGain Control) gain as well as to minimize PAPR (Peak to Average PowerRatio) degradation.

A further object of the present invention is to provide varioussequences for the communication system by designing a plurality of phaserotation factors capable of securing the same PAPR depending oncommunication bandwidths.

The technical problems solved by the present invention are not limitedto the above technical problems and other technical problems which arenot described herein will become apparent to those skilled in the artfrom the following description.

Technical Solutions

In an aspect of the present invention, provided herein is a sequencegeneration method, including: generating a basic sequence structureincluding C₅₂s, each of which is composed of 52 tones, and D₁₂s, each ofwhich is composed of 12 tones and has a non-zero value at an interval of4 tones; selecting any one from among a plurality of phase rotationfactors predetermined with respect to bandwidths for communication witha user equipment (UE); and generating the sequence to be inserted intothe preamble to be transmitted to the UE using the basic sequencestructure and the phase rotation factor. In this case, the phaserotation factor may be applied to the basic sequence structure in a unitof a C₅₂ or a C₅₂D₁₂.

The basic sequence structure may be configured in the form of aC₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂.

The phase rotation factor may be applied in the unit of the C₅₂D₁₂ tochange a phase of each C₅₂D₁₂ of the basic sequence structure and thephase rotation factor may be applied in the unit of the C₅₂ to change aphase of the remaining C₅₂.

A D₁₂ is {0, 0, 0, 1+j, 0, 0, 0, −1−j, 0, 0, 0, −1−j}.

The sequence may be generated by adding a 0₅, which is composed of fiveconsecutive 0s, to front of the basic sequence structure and adding a0₇, which is composed of seven consecutive 0s, to back of the basicsequence structure.

In a 20 MHz bandwidth, the sequence to which the 0₅ and the 0₇ are addedmay be used without any change. In a 40 MHz bandwidth, a sequencecomposed of two partial sequences, each of which is generated byeliminating the 0₅ and the 0₇ from the sequence for the 20 MHzbandwidth, one D₁₂, one 0₅, and one 0₇ may be used. In an 80 MHzbandwidth, a sequence composed of two partial sequences, each of whichis generated by eliminating the 0₅ and the 0₇ from the sequence for the40 MHz bandwidth, one D₁₂, one 0₅, and one 0₇ may be used.

In the 40 MHz bandwidth, the phase rotation factor may change phases ina unit of the partial sequence generated by eliminating the 0₅ and the0₇ from the sequence for the 20 MHz bandwidth and in the 80 MHzbandwidth, the phase rotation factor may change phases in a unit of thepartial sequence generated by eliminating the 0₅ and the 0₇ from thesequence for the 40 MHz bandwidth.

The plurality of the phase rotation factors may be generated bymultiplying any single phase rotation factor by 1, −1, i, or −i,cyclic-shifting the any single phase rotation factor, or arranging theany single phase rotation in reverse order.

The sequence generation method may further include transmitting thepreamble to the UE by inserting the generated sequence into thepreamble.

In another aspect of the present invention, provided herein is an accesspoint (AP), including: a transmitter; a receiver; and a processorconnected to the transmitter and the receiver and configured to generatethe sequence. In this case, the processor may be configured to: generatea basic sequence structure including C₅₂s, each of which is composed of52 tones, and D₁₂s, each of which is composed of 12 tones and has anon-zero value at an interval of 4 tones; select any one from among aplurality of phase rotation factors predetermined with respect tobandwidths for communication with a user equipment (UE); and generatethe sequence to be inserted into the preamble to be transmitted to theUE using the basic sequence structure and the phase rotation factor. Inaddition, the phase rotation factor may be applied to the basic sequencestructure in a unit of a C₅₂ or a C₅₂D₁₂.

Advantageous Effects

According to the embodiments of the present invention have the followingeffects.

First, improved performance of a preamble sequence can be used in a newcommunication system having an extended bandwidth.

Second, it is possible not only to obtain AGC performance gain but alsoto minimize PAPR performance degradation.

Third, a plurality of sequences are designed for each bandwidth, wherebythe communication system can select any one from among various sequencecandidates.

The effects of the present invention are not limited to theabove-described effects and other effects which are not described hereinmay be derived by those skilled in the art from the followingdescription of the embodiments of the present invention. That is,effects which are not intended by the present invention may be derivedby those skilled in the art from the embodiments of the presentinvention.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate embodiments of the inventionand together with the description serve to explain the principle of theinvention. The technical features of the present invention are notlimited to specific drawings and the features shown in the drawings arecombined to construct a new embodiment. Reference numerals of thedrawings mean structural elements.

FIG. 1 is a diagram showing an exemplary structure of an IEEE 802.11system to which the present invention is applicable;

FIG. 2 is a diagram showing another exemplary structure of an IEEE802.11 system to which the present invention is applicable;

FIG. 3 is a diagram showing another exemplary structure of an IEEE802.11 system to which the present invention is applicable;

FIG. 4 is a diagram showing an exemplary structure of a WLAN system;

FIG. 5 is a diagram illustrating a link setup process in a WLAN system;

FIG. 6 is a diagram illustrating a backoff process;

FIG. 7 is a diagram illustrating a hidden node and an exposed node;

FIG. 8 is a diagram illustrating request to send (RTS) and clear to send(CTS);

FIG. 9 is a diagram illustrating power management operation;

FIGS. 10 to 12 are diagrams illustrating operation of a station (STA)which receives a traffic indication map (TIM);

FIG. 13 is a diagram illustrating a group based association identifier(AID);

FIGS. 14 to 16 are diagrams showing examples of operation of an STA if agroup channel access interval is set;

FIG. 17 is a diagram illustrating a frame structure according to thepresent invention;

FIG. 18 is a flowchart illustrating a method for generating a sequenceaccording to proposed embodiments.

FIG. 19 is a block diagram illustrating configurations of a userequipment and a base station according to an embodiment of the presentinvention.

BEST MODE FOR INVENTION

Although the terms used in the present invention are selected fromgenerally known and used terms, terms used herein may be varieddepending on operator's intention or customs in the art, appearance ofnew technology, or the like. In addition, some of the terms mentioned inthe description of the present invention have been selected by theapplicant at his or her discretion, the detailed meanings of which aredescribed in relevant parts of the description herein. Furthermore, itis required that the present invention is understood, not simply by theactual terms used but by the meanings of each term lying within.

The following embodiments are proposed by combining constituentcomponents and characteristics of the present invention according to apredetermined format. The individual constituent components orcharacteristics should be considered optional factors on the conditionthat there is no additional remark. If required, the individualconstituent components or characteristics may not be combined with othercomponents or characteristics. In addition, some constituent componentsand/or characteristics may be combined to implement the embodiments ofthe present invention. The order of operations to be disclosed in theembodiments of the present invention may be changed. Some components orcharacteristics of any embodiment may also be included in otherembodiments, or may be replaced with those of the other embodiments asnecessary.

In describing the present invention, if it is determined that thedetailed description of a related known function or construction rendersthe scope of the present invention unnecessarily ambiguous, the detaileddescription thereof will be omitted.

In the entire specification, when a certain portion “comprises orincludes” a certain component, this indicates that the other componentsare not excluded and may be further included unless specially describedotherwise. The terms “unit”, “-or/er” and “module” described in thespecification indicate a unit for processing at least one function oroperation, which may be implemented by hardware, software or acombination thereof. The words “a or an”, “one”, “the” and words relatedthereto may be used to include both a singular expression and a pluralexpression unless the context describing the present invention(particularly, the context of the following claims) clearly indicatesotherwise.

In this document, the embodiments of the present invention have beendescribed centering on a data transmission and reception relationshipbetween a mobile station and a base station. The base station may mean aterminal node of a network which directly performs communication with amobile station. In this document, a specific operation described asperformed by the base station may be performed by an upper node of thebase station.

Namely, it is apparent that, in a network comprised of a plurality ofnetwork nodes including a base station, various operations performed forcommunication with a mobile station may be performed by the basestation, or network nodes other than the base station. The term basestation may be replaced with the terms fixed station, Node B, eNode B(eNB), advanced base station (ABS), access point, etc.

The term mobile station (MS) may be replaced with user equipment (UE),subscriber station (SS), mobile subscriber station (MSS), mobileterminal, advanced mobile station (AMS), terminal, etc.

A transmitter refers to a fixed and/or mobile node for transmitting adata or voice service and a receiver refers to a fixed and/or mobilenode for receiving a data or voice service. Accordingly, in uplink, amobile station becomes a transmitter and a base station becomes areceiver. Similarly, in downlink transmission, a mobile station becomesa receiver and a base station becomes a transmitter.

Communication of a device with a “cell” may mean that the devicetransmit and receive a signal to and from a base station of the cell.That is, although a device substantially transmits and receives a signalto a specific base station, for convenience of description, anexpression “transmission and reception of a signal to and from a cellformed by the specific base station” may be used. Similarly, the term“macro cell” and/or “small cell” may mean not only specific coverage butalso a “macro base station supporting the macro cell” and/or a “smallcell base station supporting the small cell”.

The embodiments of the present invention can be supported by thestandard documents disclosed in any one of wireless access systems, suchas an IEEE 802.xx system, a 3rd Generation Partnership Project (3GPP)system, a 3GPP Long Term Evolution (LTE) system, and a 3GPP2 system.That is, the steps or portions, which are not described in order to makethe technical spirit of the present invention clear, may be supported bythe above documents.

In addition, all the terms disclosed in the present document may bedescribed by the above standard documents. In particular, theembodiments of the present invention may be supported by at least one ofP802.16-2004, P802.16e-2005, P802.16.1, P802.16p and P802.16.1bdocuments, which are the standard documents of the IEEE 802.16 system.

Hereinafter, the preferred embodiments of the present invention will bedescribed with reference to the accompanying drawings. It is to beunderstood that the detailed description which will be disclosed alongwith the accompanying drawings is intended to describe the exemplaryembodiments of the present invention, and is not intended to describe aunique embodiment which the present invention can be carried out.

It should be noted that specific terms disclosed in the presentinvention are proposed for convenience of description and betterunderstanding of the present invention, and the use of these specificterms may be changed to another format within the technical scope orspirit of the present invention.

1. IEEE 802.11 System Overview

1.1 Structure of WLAN System

FIG. 1 is a diagram showing an exemplary structure of an IEEE 802.11system to which the present invention is applicable.

An IEEE 802.11 structure may be composed of a plurality of componentsand a wireless local area network (WLAN) supporting station (STA)mobility transparent to a higher layer may be provided by interactionamong the components. A basic service set (BSS) may correspond to abasic component block in an IEEE 802.11 LAN. In FIG. 1, two BSSs (BSS1and BSS2) are present and each BSS includes two STAs (STA1 and STA2 areincluded in BSS1 and STA3 and STA4 are included in BSS2) as members. InFIG. 1, an ellipse indicating the BSS indicates a coverage area in whichSTAs included in the BSS maintains communication. This area may bereferred to as a basic service area (BSA). If an STA moves out of a BSA,the STA cannot directly communicate with other STAs in the BSA.

In an IEEE 802.11 LAN, a BSS is basically an independent BSS (IBSS). Forexample, the IBSS may have only two STAs. In addition, the simplest BSS(BSS1 or BSS2) of FIG. 1, in which other components are omitted, maycorrespond to a representative example of the IBSS. Such a configurationis possible when STAs can directly perform communication. In addition,such a LAN is not configured in advance but may be configured if a LANis necessary. This LAN may also be referred to as an ad-hoc network.

If an STA is turned on or off or if an STA enters or moves out of a BSS,the membership of the STA in the BSS may be dynamically changed. An STAmay join a BSS using a synchronization process in order to become amember of the BSS. In order to access all services of a BSS basedstructure, an STA should be associated with the BSS. Such associationmay be dynamically set and may include use of a distribution systemservice (DSS).

FIG. 2 is a diagram showing another exemplary structure of an IEEE802.11 system to which the present invention is applicable. In FIG. 2, adistribution system (DS), a distribution system medium (DSM) and anaccess point (AP) are added to the structure of FIG. 1.

In a LAN, a direct station-to-station distance may be restricted by PHYperformance. Although such distance restriction may be possible,communication between stations located at a longer distance may benecessary. In order to support extended coverage, a DS may beconfigured.

The DS means a structure in which BSSs are mutually connected. Morespecifically, the BSSs are not independently present as shown in FIG. 1but the BSS may be present as an extended component of a networkincluding a plurality of BSSs.

The DS is a logical concept and may be specified by characteristics ofthe DSM. In IEEE 802.11 standards, a wireless medium (WM) and a DSM arelogically distinguished. Logical media are used for different purposesand are used by different components. In IEEE 802.11 standards, suchmedia are not restricted to the same or different media. Since pluralmedia are logically different, an IEEE 802.11 LAN structure (a DSstructure or another network structure) may be flexible. That is, theIEEE 802.11 LAN structure may be variously implemented and a LANstructure may be independently specified by physical properties of eachimplementation.

The DS provides seamless integration of a plurality of BSSs and provideslogical services necessary to treat an address to a destination so as tosupport a mobile apparatus.

The AP means an entity which enables associated STAs to access the DSvia the WM and has STA functionality. Data transfer between the BSS andthe DS may be performed via the AP. For example, STA2 and STA3 shown inFIG. 2 have STA functionality and provide a function enabling associatedSTAs (STA1 and STA4) to access the DS. In addition, since all APscorrespond to STAs, all APs may be addressable entities. An address usedby the AP for communication on the WM and an address used by the AP forcommunication on the DSM may not be equal.

Data transmitted from one of STAs associated with the AP to the STAaddress of the AP may always be received by an uncontrolled port andprocessed by an IEEE 802.1X port access entity. In addition, if acontrolled port is authenticated, transmission data (or frames) may betransmitted to the DS.

FIG. 3 is a diagram showing another exemplary structure of an IEEE802.11 system to which the present invention is applicable. In FIG. 3,an extended service set (ESS) for providing wide coverage is added tothe structure of FIG. 2.

A wireless network having an arbitrary size and complexity may becomposed of a DS and BSSs. In an IEEE 802.11 system, such a network isreferred to as an ESS network. The ESS may correspond to a set of BSSsconnected to one DS. However, the ESS does not include the DS. The ESSnetwork appears as an IBSS network at a logical link control (LLC)layer. STAs included in the ESS may communicate with each other andmobile STAs may move from one BSS to another BSS (within the same ESS)transparently to the LLC layer.

In IEEE 802.11, relative physical locations of the BSSs in FIG. 3 arenot assumed and may be defined as follows. The BSSs may partiallyoverlap in order to provide consecutive coverage. In addition, the BSSsmay not be physically connected and a distance between BSSs is notlogically restricted. In addition, the BSSs may be physically located atthe same location in order to provide redundancy. In addition, one (ormore) IBSS or ESS network may be physically present in the same space asone (or more) ESS network. This corresponds to an ESS network type suchas a case in which an ad-hoc network operates at a location where theESS network is present, a case in which IEEE 802.11 networks physicallyoverlapped by different organizations are configured or a case in whichtwo or more different access and security policies are necessary at thesame location.

FIG. 4 is a diagram showing an exemplary structure of a WLAN system.FIG. 4 shows an example of an infrastructure BSS including a DS.

In the example of FIG. 4, BSS1 and BSS2 configure an ESS. In the WLANsystem, an STA operates according to a MAC/PHY rule of IEEE 802.11. TheSTA includes an AP STA and a non-AP STA. The non-AP STA corresponds toan apparatus directly handled by a user, such as a laptop or a mobilephone. In the example of FIG. 4, STA1, STA3 and STA4 correspond to thenon-AP STA and STA2 and STA5 correspond to the AP STA.

In the following description, the non-AP STA may be referred to as aterminal, a wireless transmit/receive unit (WTRU), a user equipment(UE), a mobile station (MS), a mobile terminal or a mobile subscriberstation (MSS). In addition, the AP may correspond to a base station(BS), a Node-B, an evolved Node-B (eNB), a base transceiver system (BTS)or a femto BS.

1.2 Link Setup Process

FIG. 5 is a diagram illustrating a general link setup process.

In order to establish a link with respect to a network and perform datatransmission and reception, an STA discovers the network, performsauthentication, establishes association and performs an authenticationprocess for security. The link setup process may be referred to as asession initiation process or a session setup process. In addition,discovery, authentication, association and security setup of the linksetup process may be collectively referred to as an association process.

An exemplary link setup process will be described with reference to FIG.5.

In step S510, the STA may perform a network discovery operation. Thenetwork discovery operation may include a scanning operation of the STA.That is, the STA discovers the network in order to access the network.The STA should identify a compatible network before participating in awireless network and a process of identifying a network present in aspecific area is referred to as scanning. The scanning method includesan active scanning method and a passive scanning method.

In FIG. 5, a network discovery operation including an active scanningprocess is shown. In active scanning, the STA which performs scanningtransmits a probe request frame while moving between channels and waitsfor a response thereto, in order to detect which AP is present. Aresponder transmits a probe response frame to the STA, which transmittedthe probe request frame, as a response to the probe request frame. Theresponder may be an STA which lastly transmitted a beacon frame in a BSSof a scanned channel. In the BSS, since the AP transmits the beaconframe, the AP is the responder. In the IBSS, since the STAs in the IBSSalternately transmit the beacon frame, the responder is not fixed. Forexample, the STA which transmits the probe request frame on a firstchannel and receives the probe response frame on the first channelstores BSS related information included in the received probe responseframe, moves to a next channel (e.g., a second channel) and performsscanning (probe request/response transmission/reception on the secondchannel) using the same method.

Although not shown in FIG. 5, a scanning operation may be performedusing a passive scanning method. In passive scanning, the STA whichperforms scanning waits for a beacon frame while moving betweenchannels. The beacon frame is a management frame in IEEE 802.11 and isperiodically transmitted in order to indicate presence of a wirelessnetwork and to enable the STA, which performs scanning, to discover andparticipate in the wireless network. In the BSS, the AP is responsiblefor periodically transmitting the beacon frame. In the IBSS, the STAsalternately transmit the beacon frame. The STA which performs scanningreceives the beacon frame, stores information about the BSS included inthe beacon frame, and records beacon frame information of each channelwhile moving to another channel. The STA which receives the beacon framemay store BSS related information included in the received beacon frame,move to a next channel and perform scanning on the next channel usingthe same method.

Active scanning has delay and power consumption less than those ofpassive scanning.

After the STA has discovered the network, an authentication process maybe performed in step S520. Such an authentication process may bereferred to as a first authentication process to be distinguished from asecurity setup operation of step S540.

The authentication process includes a process of, at the STA,transmitting an authentication request frame to the AP and, at the AP,transmitting an authentication response frame to the STA in responsethereto. The authentication frame used for authenticationrequest/response corresponds to a management frame.

The authentication frame may include information about an authenticationalgorithm number, an authentication transaction sequence number, astatus code, a challenge text, a robust security network (RSN), a finitecyclic group, etc. The information may be examples of informationincluded in the authentication request/response frame and may bereplaced with other information. The information may further includeadditional information.

The STA may transmit the authentication request frame to the AP. The APmay determine whether authentication of the STA is allowed, based on theinformation included in the received authentication request frame. TheAP may provide the STA with the authentication result via theauthentication response frame.

After the STA is successfully authenticated, an association process maybe performed in step S530. The association process includes a processof, at the STA, transmitting an association request frame to the AP and,at the AP, transmitting an association response frame to the STA inresponse thereto.

For example, the association request frame may include information aboutvarious capabilities, beacon listen interval, service set identifier(SSID), supported rates, RSN, mobility domain, supported operatingclasses, traffic indication map (TIM) broadcast request, interworkingservice capability, etc.

For example, the association response frame may include informationabout various capabilities, status code, association ID (AID), supportedrates, enhanced distributed channel access (EDCA) parameter set,received channel power indicator (RCPI), received signal to noiseindicator (RSNI), mobility domain, timeout interval (associationcomeback time), overlapping BSS scan parameter, TIM broadcast response,QoS map, etc.

This information is purely exemplary information included in theassociation request/response frame and may be replaced with otherinformation. This information may further include additionalinformation.

After the STA is successfully authenticated, a security setup processmay be performed in step S540. The security setup process of step S540may be referred to as an authentication process through a robustsecurity network association (RSNA) request/response. The authenticationprocess of step S520 may be referred to as the first authenticationprocess and the security setup process of step S540 may be simplyreferred to as an authentication process.

The security setup process of step S540 may include a private key setupprocess through 4-way handshaking of an extensible authenticationprotocol over LAN (EAPOL) frame. In addition, the security setup processmay be performed according to a security method which is not defined inthe IEEE 802.11 standard.

2.1 Evolution of WLAN

As a technical standard recently established in order to overcomelimitations in communication speed in a WLAN, IEEE 802.11n has beendevised. IEEE 802.11n aims at increasing network speed and reliabilityand extending wireless network distance. More specifically, IEEE 802.11nis based on multiple input and multiple output (MIMO) technology usingmultiple antennas in a transmitter and a receiver in order to supporthigh throughput (HT) with a maximum data rate of 540 Mbps or more, tominimize transmission errors, and to optimize data rate.

As WLANs have come into widespread use and applications using the samehave been diversified, recently, there is a need for a new WLAN systemsupporting throughput higher than a data rate supported by IEEE 802.11n.A next-generation WLAN system supporting very high throughput (VHT) is anext version (e.g., IEEE 802.11ac) of the IEEE 802.11n WLAN system andis an IEEE 802.11 WLAN system newly proposed in order to support a datarate of 1 Gbps or more at a MAC service access point (SAP).

The next-generation WLAN system supports a multi-user MIMO (MU-MIMO)transmission scheme by which a plurality of STAs simultaneously accessesa channel in order to efficiently use a radio channel. According to theMU-MIMO transmission scheme, the AP may simultaneously transmit packetsto one or more MIMO-paired STAs.

In addition, support of a WLAN system operation in a whitespace is beingdiscussed. For example, introduction of a WLAN system in a TV whitespace(WS) such as a frequency band (e.g., 54 to 698 MHz) in an idle state dueto digitalization of analog TVs is being discussed as the IEEE 802.11afstandard. However, this is only exemplary and the whitespace may beincumbently used by a licensed user. The licensed user means a user whois allowed to use a licensed band and may be referred to as a licenseddevice, a primary user or an incumbent user.

For example, the AP and/or the STA which operate in the WS shouldprovide a protection function to the licensed user. For example, if alicensed user such as a microphone already uses a specific WS channelwhich is a frequency band divided on regulation such that a WS band hasa specific bandwidth, the AP and/or the STA cannot use the frequencyband corresponding to the WS channel in order to protect the licenseduser. In addition, the AP and/or the STA must stop use of the frequencyband if the licensed user uses the frequency band used for transmissionand/or reception of a current frame.

Accordingly, the AP and/or the STA should perform a procedure ofdetermining whether a specific frequency band in a WS band is available,that is, whether a licensed user uses the frequency band. Determiningwhether a licensed user uses a specific frequency band is referred to asspectrum sensing. As a spectrum sensing mechanism, an energy detectionmethod, a signature detection method, etc. may be used. It may bedetermined that the licensed user uses the frequency band if receivedsignal strength is equal to or greater than a predetermined value or ifa DTV preamble is detected.

In addition, as next-generation communication technology,machine-to-machine (M2M) communication technology is being discussed.Even in an IEEE 802.11 WLAN system, a technical standard supporting M2Mcommunication has been developed as IEEE 802.11ah. M2M communicationmeans a communication scheme including one or more machines and may bereferred to as machine type communication (MTC). Here, a machine meansan entity which does not require direct operation or intervention of aperson. For example, a device including a mobile communication module,such as a meter or a vending machine, may include a user equipment suchas a smart phone which is capable of automatically accessing a networkwithout operation/intervention of a user to perform communication. M2Mcommunication includes communication between devices (e.g.,device-to-device (D2D) communication) and communication between a deviceand an application server. Examples of communication between a deviceand a server include communication between a vending machine and aserver, communication between a point of sale (POS) device and a serverand communication between an electric meter, a gas meter or a watermeter and a server. An M2M communication based application may includesecurity, transportation, health care, etc. If the characteristics ofsuch examples are considered, in general, M2M communication shouldsupport transmission and reception of a small amount of data at a lowrate in an environment in which very many apparatuses are present.

More specifically, M2M communication should support a larger number ofSTAs. In a currently defined WLAN system, it is assumed that a maximumof 2007 STAs is associated with one AP. However, in M2M communication,methods supporting the case in which a larger number of STAs (about6000) are associated with one AP are being discussed. In addition, inM2M communication, it is estimated that there are many applicationssupporting/requiring a low transfer rate. In order to appropriatelysupport the low transfer rate, for example, in a WLAN system, the STAmay recognize presence of data to be transmitted thereto based on atraffic indication map (TIM) element and methods of reducing a bitmapsize of the TIM are being discussed. In addition, in M2M communication,it is estimated that there is traffic having a very longtransmission/reception interval. For example, in electricity/gas/waterconsumption, a very small amount of data is required to be exchanged ata long period (e.g., one month). In a WLAN system, although the numberof STAs associated with one AP is increased, methods of efficientlysupporting the case in which the number of STAs, in which a data frameto be received from the AP is present during one beacon period, is verysmall are being discussed.

WLAN technology has rapidly evolved. In addition to the above-describedexamples, technology for direct link setup, improvement of mediastreaming performance, support of fast and/or large-scale initialsession setup, support of extended bandwidth and operating frequency,etc. is being developed.

2.2 Medium Access Mechanism

In a WLAN system according to IEEE 802.11, the basic access mechanism ofmedium access control (MAC) is a carrier sense multiple access withcollision avoidance (CSMA/CA) mechanism. The CSMA/CA mechanism is alsoreferred to as a distributed coordination function (DCF) of IEEE 802.11MAC and employs a “listen before talk” access mechanism. According tosuch an access mechanism, the AP and/or the STA may perform clearchannel assessment (CCA) for sensing a radio channel or medium during apredetermined time interval (for example, a DCF inter-frame space(DIFS)) before starting transmission. If it is determined that themedium is in an idle state as the sensed result, frame transmissionstarts via the medium. If it is determined that the medium is in anoccupied state, the AP and/or the STA may set and wait for a delayperiod (e.g., a random backoff period) for medium access withoutstarting transmission and then attempt to perform frame transmission.Since several STAs attempt to perform frame transmission after waitingfor different times by applying the random backoff period, it ispossible to minimize collision.

In addition, the IEEE 802.11 MAC protocol provides a hybrid coordinationfunction (HCF). The HCF is based on the DCF and a point coordinationfunction (PCF). The PCF refers to a periodic polling method for enablingall reception AP and/or STAs to receive data frames using a pollingbased synchronous access method. In addition, the HCF has enhanceddistributed channel access (EDCA) and HCF controlled channel access(HCCA). The EDCA uses a contention access method for providing dataframes to a plurality of users by a provider and the HCCA uses acontention-free channel access method using a polling mechanism. Inaddition, the HCF includes a medium access mechanism for improvingquality of service (QoS) of a WLAN and may transmit QoS data both in acontention period (CP) and a contention free period (CFP).

FIG. 6 is a diagram illustrating a backoff process.

Operation based on a random backoff period will be described withreference to FIG. 6. If a medium is changed from an occupied or busystate to an idle state, several STAs may attempt data (or frame)transmission. At this time, a method of minimizing collision, the STAsmay select respective random backoff counts, wait for slot timescorresponding to the random backoff counts and attempt transmission. Therandom backoff count has a pseudo-random integer and may be set to oneof values of 0 to CW. Here, the CW is a contention window parametervalue. The CW parameter is set to CWmin as an initial value but may beset to twice CWmin if transmission fails (e.g., ACK for the transmissionframe is not received). If the CW parameter value becomes CWmax, datatransmission may be attempted while maintaining the CWmax value untildata transmission is successful. If data transmission is successful, theCW parameter value is reset to CWmin. CW, CWmin and CWmax values arepreferably set to 2n−1 (n=0, 1, 2, . . . ).

If the random backoff process starts, the STA continuously monitors themedium while the backoff slots are counted down according to the setbackoff count value. If the medium is in the occupied state, countdownis stopped and, if the medium is in the idle state, countdown isresumed.

In the example of FIG. 6, if packets to be transmitted to the MAC ofSTA3 arrive, STA3 may confirm that the medium is in the idle stateduring the DIFS and immediately transmit a frame. Meanwhile, theremaining STAs monitor that the medium is in the busy state and wait.During a wait time, data to be transmitted may be generated in STA1,STA2 and STA5. The STAs may wait for the DIFS if the medium is in theidle state and then count down the backoff slots according to therespectively selected random backoff count values.

In the example of FIG. 6, STA2 selects a smallest backoff count valueand STA1 selects a largest backoff count value. That is, the residualbackoff time of STA5 is less than the residual backoff time of STA1 whenSTA2 completes backoff count and starts frame transmission. STA1 andSTA5 stop countdown and wait while STA2 occupies the medium. Ifoccupancy of the medium by STA2 ends and the medium enters the idlestate again, STA1 and STA5 wait for the DIFS and then resume countdown.That is, after the residual backoff slots corresponding to the residualbackoff time are counted down, frame transmission may start. Since theresidual backoff time of STA5 is less than of STA1, STA5 starts frametransmission.

If STA2 occupies the medium, data to be transmitted may be generated inthe STA4. At this time, STA4 may wait for the DIFS if the medium entersthe idle state, perform countdown according to a random backoff countvalue selected thereby, and start frame transmission. In the example ofFIG. 6, the residual backoff time of STA5 accidentally matches therandom backoff time of STA4. In this case, collision may occur betweenSTA4 and STA5. If collision occurs, both STA4 and STA5 do not receiveACK and data transmission fails. In this case, STA4 and STA5 may doublethe CW value, select the respective random backoff count values and thenperform countdown. STA1 may wait while the medium is busy due totransmission of STA4 and STA5, wait for the DIFS if the medium entersthe idle state, and start frame transmission if the residual backofftime has elapsed.

2.3 Sensing Operation of STA

As described above, the CSMA/CA mechanism includes not only physicalcarrier sensing for directly sensing a medium by an AP and/or an STA butalso virtual carrier sensing. Virtual carrier sensing solves a problemwhich may occur in medium access, such as a hidden node problem. Forvirtual carrier sensing, MAC of a WLAN may use a network allocationvector (NAV). The NAV refers to a value of a time until a medium becomesavailable, which is indicated to another AP and/or STA by an AP and/oran STA, which is currently utilizing the medium or has rights to utilizethe medium. Accordingly, the NAV value corresponds to a period of timewhen the medium will be used by the AP and/or the STA for transmittingthe frame, and medium access of the STA which receives the NAV value isprohibited during that period of time. The NAV may be set according tothe value of the “duration” field of a MAC header of a frame.

A robust collision detection mechanism for reducing collision has beenintroduced, which will be described with reference to FIGS. 7 and 8.Although a transmission range may not be equal to an actual carriersensing range, for convenience, assume that the transmission range maybe equal to the actual carrier sensing range.

FIG. 7 is a diagram illustrating a hidden node and an exposed node.

FIG. 7(a) shows a hidden node, and, in this case, an STA A and an STA Bare performing communication and an STA C has information to betransmitted. More specifically, although the STA A transmits informationto the STA B, the STA C may determine that the medium is in the idlestate, when carrier sensing is performed before transmitting data to theSTA B. This is because the STA C may not sense transmission of the STA A(that is, the medium is busy). In this case, since the STA Bsimultaneously receives information of the STA A and the STA C,collision occurs. At this time, the STA A may be the hidden node of theSTA C.

FIG. 7(b) shows an exposed node and, in this case, the STA B transmitsdata to the STA A and the STA C has information to be transmitted to theSTA D. In this case, if the STA C performs carrier sensing, it may bedetermined that the medium is busy due to transmission of the STA B. Ifthe STA C has information to be transmitted to the STA D, since it issensed that the medium is busy, the STA C waits until the medium entersthe idle state. However, since the STA A is actually outside thetransmission range of the STA C, transmission from the STA C andtransmission from the STA B may not collide from the viewpoint of theSTA A. Therefore, the STA C unnecessarily waits until transmission ofthe STA B is stopped. At this time, the STA C may be the exposed node ofthe STA B.

FIG. 8 is a diagram illustrating request to send (RTS) and clear to send(CTS).

In the example of FIG. 7, in order to efficiently use a collisionavoidance mechanism, short signaling packet such as RTS and CTS may beused. RST/CTS between two STAs may be enabled to be overheard byperipheral STAs such that the peripheral STAs confirm informationtransmission between the two STAs. For example, if a transmission STAtransmits an RTS frame to a reception STA, the reception STA transmits aCTS frame to peripheral UEs to inform the peripheral UEs that thereception STA receives data.

FIG. 8(a) shows a method of solving a hidden node problem. Assume thatboth the STA A and the STA C attempt to transmit data to the STA B. Ifthe STA A transmits the RTS to the STA B, the STA B transmits the CTS tothe peripheral STA A and C. As a result, the STA C waits until datatransmission of the STA A and the STA B is finished, thereby avoidingcollision.

FIG. 8(b) shows a method of solving an exposed node problem. The STA Cmay overhear RTS/CTS transmission between the STA A and the STA B anddetermine that collision does not occur even when the STA C transmitsdata to another STA (e.g., the STA D). That is, the STA B transmits theRTS to all peripheral UEs and transmits the CTS only to the STA A havingdata to be actually transmitted. Since the STA C receives the RTS butdoes not receive the CTS of the STA A, it can be confirmed that the STAA is outside carrier sensing of the STA C.

2.4 Power Management

As described above, in a WLAN system, channel sensing should beperformed before an STA performs transmission and reception. When thechannel is always sensed, continuous power consumption of the STA iscaused. Power consumption in a reception state is not substantiallydifferent from power consumption in a transmission state andcontinuously maintaining the reception state imposes a burden on an STAwith limited power (that is, operated by a battery). Accordingly, if areception standby state is maintained such that the STA continuouslysenses the channel, power is inefficiently consumed without any specialadvantage in terms of WLAN throughput. In order to solve such a problem,in a WLAN system, a power management (PM) mode of the STA is supported.

The PM mode of the STA is divided into an active mode and a power save(PS) mode. The STA fundamentally operates in an active mode. The STAwhich operates in the active mode is maintained in an awake state. Theawake state refers to a state in which normal operation such as frametransmission and reception or channel scanning is possible. The STAwhich operates in the PS mode operates while switching between a sleepstate or an awake state. The STA which operates in the sleep stateoperates with minimum power and does not perform frame transmission andreception or channel scanning.

Since power consumption is reduced as the sleep state of the STA isincreased, the operation period of the STA is increased. However, sinceframe transmission and reception is impossible in the sleep state, theSTA may not unconditionally operate in the sleep state. If a frame to betransmitted from the STA, which operates in the sleep state, to the APis present, the STA may be switched to the awake state to transmit theframe. If a frame to be transmitted from the AP to the STA is present,the STA in the sleep state may not receive the frame and may not confirmthat the frame to be received is present. Accordingly, the STA needs toperform an operation for switching to the awake state according to aspecific period in order to confirm presence of the frame to betransmitted thereto (to receive the frame if the frame to be transmittedis present).

FIG. 9 is a diagram illustrating power management operation.

Referring to FIG. 9, an AP 210 transmits beacon frames to STAs within aBSS at a predetermined period (S211, S212, S213, S214, S215 and S216).The beacon frame includes a traffic indication map (TIM) informationelement. The TIM information element includes information indicatingthat buffered traffic for STAs associated with the AP 210 is present andthe AP 210 will transmit a frame. The TIM element includes a TIM used toindicate a unicast frame or a delivery traffic indication map (DTIM)used to indicate a multicast or broadcast frame.

The AP 210 may transmit the DTIM once whenever the beacon frame istransmitted three times. An STA1 220 and an STA2 222 operate in the PSmode. The STA1 220 and the STA2 222 may be switched from the sleep stateto the awake state at a predetermined wakeup interval to receive a TIMelement transmitted by the AP 210. Each STA may compute a time to switchto the awake state based on a local clock thereof. In the example ofFIG. 9, assume that the clock of the STA matches the clock of the AP.

For example, the predetermined awake interval may be set such that theSTA1 220 is switched to the awake state every beacon interval to receivea TIM element. Accordingly, the STA1 220 may be switched to the awakestate (S211) when the AP 210 first transmits the beacon frame (S211).The STA1 220 may receive the beacon frame and acquire the TIM element.If the acquired TIM element indicates that a frame to be transmitted tothe STA1 220 is present, the STA1 220 may transmit, to the AP 210, apower save-Poll (PS-Poll) frame for requesting frame transmission fromthe AP 210 (S221 a). The AP 210 may transmit the frame to the STA1 220in correspondence with the PS-Poll frame (S231). The STA1 220 whichcompletes frame reception is switched to the sleep state.

When the AP 210 secondly transmits the beacon frame, since anotherdevice access the medium and thus the medium is busy, the AP 210 may nottransmit the beacon frame at an accurate beacon interval and maytransmit the beacon frame at a delayed time (S212). In this case, theoperation mode of the STA1 220 is switched to the awake state accordingto the beacon interval but the delayed beacon frame is not received.Therefore, the operation mode of the STA1 220 is switched to the sleepstate again (S222).

When the AP 210 thirdly transmits the beacon frame, the beacon frame mayinclude a TIM element set to a DTIM. Since the medium is busy, the AP210 transmits the beacon frame at a delayed time (S213). The STA1 220 isswitched to the awake state according to the beacon interval and mayacquire the DTIM via the beacon frame transmitted by the AP 210. Assumethat the DTIM acquired by the STA1 220 indicates that a frame to betransmitted to the STA1 220 is not present and a frame for another STAis present. In this case, the STA1 220 may confirm that a frametransmitted thereby is not present and may be switched to the sleepstate again. The AP 210 transmits the beacon frame and then transmitsthe frame to the STA (S232).

The AP 210 fourthly transmits the beacon frame (S214). Since the STA1220 cannot acquire information indicating that buffered traffictherefore is present via reception of the TIM element twice, the wakeupinterval for receiving the TIM element may be controlled. Alternatively,if signaling information for controlling the wakeup interval of the STA1220 is included in the beacon frame transmitted by the AP 210, thewakeup interval value of the STA1 220 may be controlled. In the presentexample, the STA1 220 may change switching of the operation state forreceiving the TIM element every beacon interval to switching of theoperation state every three beacon intervals. Accordingly, since theSTA1 220 is maintained in the sleep state when the AP 210 transmits thefourth beacon frame (S214) and transmits the fifth beacon frame (S215),the TIM element cannot be acquired.

When the AP 210 sixthly transmits the beacon frame (S216), the STA1 220may be switched to the awake state to acquire the TIM element includedin the beacon frame (S224). Since the TIM element is a DTIM indicatingthat a broadcast frame is present, the STA1 220 may not transmit thePS-Poll frame to the AP 210 but may receive a broadcast frametransmitted by the AP 210 (S234). The wakeup interval set in the STA2230 may be set to be greater than that of the STA1 220. Accordingly, theSTA2 230 may be switched to the awake state to receive the TIM element(S241), when the AP 210 fifthly transmits the beacon frame (S215). TheSTA2 230 may confirm that a frame to be transmitted thereto is presentvia the TIM element and transmits the PS-Poll frame to the AP 210 (S241a) in order to request frame transmission. The AP 210 may transmit theframe to the STA2 230 in correspondence with the PS-Poll frame (S233).

For PM management shown in FIG. 9, a TIM element includes a TIMindicating whether a frame to be transmitted to an STA is present and aDTIM indicating whether a broadcast/multicast frame is present. The DTIMmay be implemented by setting a field of the TIM element.

FIGS. 10 to 12 are diagrams illustrating operation of a station (STA)which receives a traffic indication map (TIM).

Referring to FIG. 10, an STA may be switched from a sleep state to anawake state in order to receive a beacon frame including a TIM from anAP and interpret the received TIM element to confirm that bufferedtraffic to be transmitted thereto is present. The STA may contend withother STAs for medium access for transmitting a PS-Poll frame and thentransmit the PS-Poll frame in order to request data frame transmissionfrom the AP. The AP which receives the PS-Poll frame transmitted by theSTA may transmit the frame to the STA. The STA may receive the dataframe and transmit an ACK frame to the AP. Thereafter, the STA may beswitched to the sleep state again.

As shown in FIG. 10, the AP may receive the PS-Poll frame from the STAand then operate according to an immediate response method fortransmitting a data frame after a predetermined time (e.g., a shortinter-frame space (SIFS)). If the AP does not prepare a data frame to betransmitted to the STA during the SIFS after receiving the PS-Pollframe, the AP may operate according to a deferred response method, whichwill be described with reference to FIG. 11.

In the example of FIG. 11, operation for switching the STA from thesleep state to the awake state, receiving a TIM from the AP, contendingand transmitting a PS-Poll frame to the AP is equal to that of FIG. 10.If the data frame is not prepared during the SIFS even when the APreceives the PS-Poll frame, the data frame is not transmitted but an ACKframe may be transmitted to the STA. If the data frame is prepared aftertransmitting the ACK frame, the AP may contend and transmit the dataframe to the STA. The STA may transmit the ACK frame indicating that thedata frame has been successfully received to the AP and may be switchedto the sleep state.

FIG. 12 shows an example in which the AP transmits the DTIM. The STAsmay be switched from the sleep state to the awake state in order toreceive the beacon frame including the DTIM element from the AP. The STAmay confirm that a multicast/broadcast frame will be transmitted via thereceived DTIM. The AP may immediately transmit data (that is, amulticast/broadcast frame) without PS-Poll frame transmission andreception after transmitting the beacon frame including the DTIM. TheSTAs may receive data in the awake state after receiving the beaconframe including the DTIM and may be switched to the sleep state againafter completing data reception.

2.5 TIM Structure

In the PM mode management method based on the TIM (or DTIM) protocoldescribed with reference to FIGS. 9 to 12, the STAs may confirm whethera data frame to be transmitted thereto is present via STA identificationincluded in the TIM element. The STA identification may be related to anassociation identifier (AID) assigned to the STA upon association withthe AP.

The AID is used as a unique identifier for each STA within one BSS. Forexample, in a current WLAN system, the AID may be one of values of 1 to2007. In a currently defined WLAN system, 14 bits are assigned to theAID in a frame transmitted by the AP and/or the STA. Although up to16383 may be assigned as the AID value, 2008 to 16383 may be reserved.

The TIM element according to an existing definition is not appropriatelyapplied to an M2M application in which a large number (e.g., more than2007) of STAs is associated with one AP. If the existing TIM structureextends without change, the size of the TIM bitmap is too large to besupported in an existing frame format and to be suitable for M2Mcommunication considering an application with a low transfer rate. Inaddition, in M2M communication, it is predicted that the number of STAs,in which a reception data frame is present during one beacon period, isvery small. Accordingly, in M2M communication, since the size of the TIMbitmap is increased but most bits have a value of 0, there is a need fortechnology for efficiently compressing the bitmap.

As an existing bitmap compression technology, a method of omitting 0which continuously appears at a front part of a bitmap and defining anoffset (or a start point) is provided. However, if the number of STAs inwhich a buffered frame is present is small but a difference between theAID values of the STAs is large, compression efficiency is bad. Forexample, if only frames to be transmitted to only two STAs respectivelyhaving AID values of 10 and 2000 are buffered, the length of thecompressed bitmap is 1990 but all bits other than both ends have a valueof 0. If the number of STAs which may be associated with one AP issmall, bitmap compression inefficiency is not problematic but, if thenumber of STAs is increased, bitmap compression inefficiencydeteriorates overall system performance.

As a method of solving this problem, AIDs may be divided into severalgroups to more efficiently perform data transmission. A specific groupID (GID) is assigned to each group. AIDs assigned based on the groupwill be described with reference to FIG. 13.

FIG. 13(a) shows an example of AIDs assigned based on a group. In theexample of FIG. 13(a), several bits of a front part of the AID bitmapmay be used to indicate the GID. For example, four DIDs may be expressedby the first two bits of the AID of the AID bitmap. If the total lengthof the AID bitmap is N bits, the first two bits (B1 and B2) indicate theGID of the AID.

FIG. 13(a) shows another example of AIDs assigned based on a group. Inthe example of FIG. 13(b), the GID may be assigned according to thelocation of the AID. At this time, the AIDs using the same GID may beexpressed by an offset and a length value. For example, if GID 1 isexpressed by an offset A and a length B, this means that AIDs of A toA+B−1 on the bitmap have GID 1. For example, in the example of FIG.13(b), assume that all AIDs of 1 to N4 are divided into four groups. Inthis case, AIDs belonging to GID 1 are 1 to N1 and may be expressed byan offset 1 and a length N1. AIDS belonging to GID2 may be expressed byan offset N1+1 and a length N2−N1+1, AIDs belonging to GID 3 may beexpressed by an offset N2+1 and a length N3−N2+1. and AIDs belonging toGID 4 may be expressed by an offset N3+1 and a length N4−N3+1.

If the AIDs assigned based on the group are introduced, channel accessis allowed at a time interval which is changed according to the GID tosolve lack of TIM elements for a large number of STAs and to efficientlyperform data transmission and reception. For example, only channelaccess of STA(s) corresponding to a specific group may be granted duringa specific time interval and channel access of the remaining STA(s) maybe restricted. A predetermined time interval at which only access ofspecific STA(s) is granted may also be referred to as a restrictedaccess window (RAW).

Channel access according to GID will be described with reference to FIG.13(c). FIG. 13(c) shows a channel access mechanism according to a beaconinterval if the AIDs are divided into three groups. At a first beaconinterval (or a first RAW), channel access of STAs belonging to GID 1 isgranted but channel access of STAs belonging to other GIDs is notgranted. For such implementation, the first beacon includes a TIMelement for AIDs corresponding to GID 1. A second beacon frame includesa TIM element for AIDs corresponding to GID 2 and thus only channelaccess of the STAs corresponding to the AIDs belonging to GID 2 isgranted during the second beacon interval (or the second RAW). A thirdbeacon frame includes a TIM element for AIDs corresponding to GID 3 andthus only channel access of the STAs corresponding to the AIDs belongingto GID 3 is granted during the third beacon interval (or the third RAW).A fourth beacon frame includes a TIM element for AIDs corresponding toGID 1 and thus only channel access of the STAs corresponding to the AIDsbelonging to GID 1 is granted during the fourth beacon interval (or thefourth RAW). Only channel access of the STAs corresponding to a specificgroup indicated by the TIM included in the beacon frame may be grantedeven in fifth and subsequent beacon intervals (or fifth and subsequentRAWs).

Although the order of GIDs allowed according to the beacon interval iscyclic or periodic in FIG. 13(c), the present invention is not limitedthereto. That is, by including only AID(s) belonging to specific GID(s)in the TIM elements, only channel access of STA(s) corresponding to thespecific AID(s) may be granted during a specific time interval (e.g., aspecific RAW) and channel access of the remaining STA(s) may not begranted.

The above-described group based AID assignment method may also bereferred to as a hierarchical structure of a TIM. That is, an entire AIDspace may be divided into a plurality of blocks and only channel accessof STA(s) corresponding to a specific block having a non-zero value(that is, STAs of a specific group) may be granted. A TIM having a largesize is divided into small blocks/groups such that the STA easilymaintains TIM information and easily manages blocks/groups according toclass, QoS or usage of the STA. Although a 2-level layer is shown in theexample of FIG. 13, a TIM of a hierarchical structure having two or morelevels may be constructed. For example, the entire AID space may bedivided into a plurality of page groups, each page group may be dividedinto a plurality of blocks, and each block may be divided into aplurality of sub-blocks. In this case, as an extension of the example ofFIG. 13(a), the first N1 bits of the AID bitmap indicate a paging ID(that is, a PID), the next N2 bits indicate a block ID, the next N3 bitsindicate a sub-block ID, and the remaining bits indicate the STA bitlocation in the sub-block.

In the following examples of the present invention, various methods ofdividing and managing STAs (or AIDs assigned to the STAs) on apredetermined hierarchical group basis are applied and the group basedAID assignment method is not limited to the above examples.

2.6 Improved Channel Access Method

If AIDs are assigned/managed based on a group, STAs belonging to aspecific group may use a channel only at a “group channel accessinterval (or RAW)” assigned to the group. If an STA supports an M2Mapplication, traffic for the STA may have a property which may begenerated at a long period (e.g., several tens of minutes or severalhours). Since such an STA does not need to be in the awake statefrequently, the STA may be in the sleep mode for g a long period of timeand be occasionally switched to the awake state (that is, the awakeinterval of the STA may be set to be long). An STA having a long wakeupinterval may be referred to as an STA which operates in a “long-sleeper”or “long-sleep” mode. The case in which the wakeup interval is set to belong is not limited to M2M communication and the wakeup interval may beset to be long according to the state of the STA or surroundings of theSTA even in normal WLAN operation.

If the wakeup interval is set, the STA may determine whether a localclock thereof exceeds the wakeup interval. However, since the localclock of the STA generally uses a cheap oscillator, an error probabilityis high. In addition, if the STA operates in long-sleep mode, the errormay be increased with time. Accordingly, time synchronization of the STAwhich occasionally wakes up may not match time synchronization of theAP. For example, although the STA computes when the STA may receive thebeacon frame to be switched to the awake state, the STA may not actuallyreceive the beacon frame from the AP at that timing. That is, due toclock drift, the STA may miss the beacon frame and such a problem mayfrequently occur if the STA operates in the long sleep mode.

FIGS. 14 to 16 are diagrams showing examples of operation of an STA if agroup channel access interval is set.

In the example of FIG. 14, STA3 may belong to group 3 (that is, GID=3),wake up at a channel access interval assigned to group 1 and performPS-Poll for requesting frame transmission from the AP. The AP whichreceives PS-Poll from the STA transmits an ACK frame to STA3. Ifbuffered data to be transmitted to STA3 is present, the AP may provideinformation indicating that data to be transmitted is present via theACK frame. For example, the value of a “More Data” field (or an MDfield) having a size of 1 bit included in the ACK frame may be set to 1(that is, MD=1) to indicate the above information.

Since a time when STA3 transmits PS-Poll belongs to the channel accessinterval for group 1, even if data to be transmitted to STA3 is present,the AP does not immediately transmit data after transmitting the ACKframe but transmits data to STA3 at a channel access interval (GID 3channel access of FIG. 14) assigned to group 3 to which STA3 belongs.

Since STA3 receives the ACK frame set to MD=1 from the AP, STA3continuously waits for transmission of data from the AP. That is, in theexample of FIG. 14, since STA3 cannot receive the beacon frameimmediately after waking up, STA3 transmits PS-Poll to the AP on theassumption that a time when STA3 wakes up corresponds to the channelaccess interval assigned to the group, to which STA3 belongs, accordingto computation based on the local clock thereof and data to betransmitted thereto is present. Alternatively, since STA3 operates inthe long-sleep mode, on the assumption that time synchronization is notperformed, if the data to be transmitted thereto is present, STA3 maytransmit PS-Poll to the AP in order to receive the data. Since the ACKframe received by STA3 from the AP indicates that data to be transmittedto STA3 is present, STA3 continuously waits for data reception under theassumption of the interval in which channel access thereof is granted.STA3 unnecessarily consumes power even when data reception is notallowed, until time synchronization is appropriately performed frominformation included in a next beacon frame.

In particular, if STA3 operates in the long-sleep mode, the beacon framemay frequently not be received, CCA may be performed even at the channelaccess interval, to which STA2 does not belong, thereby causingunnecessary power consumption.

Next, in the example of FIG. 15, the beacon frame is missed when the STAhaving GID 1 (that is, belonging to group 1) wakes up. That is, the STAwhich does not receive the beacon frame including the GID (or PID)assigned thereto is continuously in the awake state until the beaconframe including the GID (or PID) thereof is received. That is, althoughthe STA wakes up at channel access interval assigned thereto, the STAcannot confirm whether the GID (or PID) thereof is included in the TIMtransmitted via the beacon frame and thus cannot confirm whether thetiming corresponds to the channel access interval assigned to the groupthereof.

In the example of FIG. 15, the STA which is switched from the sleepstate to the awake state is continuously in the awake state until thefourth beacon frame including the GID (that is, GID 1) thereof isreceived after the first beacon frame has been missed, thereby causingunnecessary power consumption. As a result, after unnecessary powerconsumption, the STA may receive the beacon frame including GID 1 andthen may perform RTS transmission, CTS reception, data frametransmission and ACK reception.

FIG. 16 shows the case in which an STA wakes up at a channel accessinterval for another group. For example, the STA having GID 3 may wakeup at the channel access interval for GID 1. That is, the STA having GID3 unnecessarily consumes power until the beacon frame having the GIDthereof is received after waking up. If a TIM indicating GID 3 isreceived via a third beacon frame, the STA may recognize the channelaccess interval for the group thereof and perform data transmission andACK reception after CCA through RTS and CTS.

3. Proposed Sequence Generation Method

In the conventional WiFi standards, sequences are defined respectivelyfor a short training filed (STF) and a long training filed (LTF). Inparticular, different STF and LTF sequences are defined for individualbandwidths of 20, 40, and 80 MHz. In addition, a phase rotation factor,which is applied to the STF and LTF sequences when a bandwidth isextended, is defined to have a different value for individual bandwidthsof 20, 40, and 80 MHz.

As interest in future Wi-Fi and demand for improvement of throughput andQoE (quality of experience) after 802.11ac increase, it is necessary todefine a new frame format for future WLAN systems. The most importantpart in a new frame format is a preamble part because design of apreamble used for synchronization, channel tracking, channel estimation,adaptive gain control (AGC) and the like may directly affect systemperformance.

In the future Wi-Fi system in which a large number of APs and STAssimultaneously access and attempt data transmission and reception,system performance may be limited when legacy preamble design isemployed. That is, if each preamble block (e.g., a short training field(STF) in charge of AGC, CFO estimation/compensation, timing control andthe like or a long training field (LTF) in charge of channelestimation/compensation, residual CFO compensation and the like)executes only the function thereof defined in the legacy preamblestructure, frame length increases, causing overhead. Accordingly, if aspecific preamble block can support various functions in addition to thefunction designated therefore, an efficient frame structure can bedesigned.

Furthermore, since the future Wi-Fi system considers data transmissionin outdoor environments as well as indoor environments, the preamblestructure may need to be designed differently depending on environments.Although design of a unified preamble format independent of environmentvariation can aid in system implementation and operation, of course, itis desirable that preamble design be adapted to system environment.

Preamble design for efficiently supporting various functions isdescribed hereinafter. For convenience, a new WLAN system is referred toas an HE (High Efficiency) system and a frame and a PPDU (PLCP (PhysicalLayer Convergence Procedure) Protocol Data Unit) of the HE system arerespectively referred to as an HE frame and an HE PPDU. However, it isobvious to those skilled in the art that the proposed preamble isapplicable to other WLAN systems and cellular systems in addition to theHE system.

The following table 1 shows OFDM numerology which is a premise of apilot sequence transmission method described below. Table 1 shows anexample of new OFDM numerology proposed in the HE system and numeralsand items shown in Table 1 are merely examples and other values may beapplied. Table 1 is based on the assumption that FFT having a size fourtimes the legacy one is applied to a given BW and 3 DCs are used per BW.

TABLE 1 Parameter CBW20 CBW40 CBW80 CBW80 + 80 CBW160 DescriptionN_(FFT) 256 512 1024 1024 2048 FFT size N_(SD) 238 492 1002 1002 2004Number of complex data numbers per frequency segment N_(SP) 4 6 8 8 16Number of pilot values per frequency segment N_(ST) 242 498 1010 10102020 Total number of subcarriers per frequency segment. See NOTE. N_(SR)122 250 506 506 1018 Highest data subcarrier index per frequency segmentN_(Seg) 1 1 1 2 1 Number of frequency segments Δ_(F) 312.5 kHz Subcarrier frequency Spacing for non-HE portion Δ_(F) _(—) _(HE) 78.125kHz   Subcarrier frequency Spacing for HE portion T_(DFT) 3.2 μsIDFT/DFT period for non-HE portion T_(DFT) _(—) _(HE) 12.8 μs  IDFT/DFTperiod for HE portion T_(GI) 0.8 μs = T_(DFT)/4 Guard interval durationfor non- HE portion T_(GI) _(—) _(HE) 3.2 μs = T_(DFT) _(—) _(HE)/4Guard interval duration for HE portion T_(GI2) 1.6 μs Double guardinterval for non-HE portion T_(GIS) _(—) _(HE) 0.8 μs = T_(DFT HE)/16[Alternative: 0.4 μs (1/32 CP)] Short guard interval Duration (used onlyfor HE data) T_(SYML) 4 μs = T_(DFT) + T_(GI) Long GI symbol intervalfor non-HE portion T_(SYML) _(—) _(HE) 16 μs = T_(DFT) _(—) _(HE) +T_(GI) _(—) _(HE) Long GI symbol interval for HE portion T_(SYMS) _(—)_(HE) 13.6 μs = T_(DFT) _(—) _(HE) + T_(GIS) _(—) _(HE) [Alternative:13.2 μs (with 1/32 CP)] Short GI symbol interval (used only for HE data)T_(SYM) T_(SYML) or T_(SYMS) depending on the GI used Symbol intervalfor non-HE portion T_(SYM) _(—) _(HE) T_(SYML) _(—) _(HE) or T_(SYMS)_(—) _(HE) depending on the GI used Symbol interval for HE portionT_(L-STF) 8 μs = 10 * T_(DFT)/4 Non-HE Short Training field durationT_(L-LTF) 8 μs = 2 × T_(DFT) + T_(GI2) Non-HE Long Training fieldduration T_(L-SIG) 4 μs = T_(SYML) Non-HE SIGNAL field durationT_(HE-SIGA) 12.8 μs = 2(T_(SYML) + 3T_(GI)) in HE- PPDU format-1 orT_(SYML HE) in HE- HE Signal A field PPDU format-2 and HE-PPDU format-3duration T_(HE-STF) T_(SYML) _(—) _(HE) HE Short Training field durationT_(HE-LTF) T_(SYML) _(—) _(HE) Duration of each HE LTF symbolT_(HE-SIGB) T_(SYML) _(—) _(HE) HE Signal B field duration N_(service)16 Number of bits in the SERVICE field N_(tail)  6 Number of tail bitsper BCC encoder NOTE— N_(ST) = N_(SD) + N_(SP)

FIG. 17 is a diagram illustrating frame structures related to anembodiment of the present invention. As illustrated in FIGS. 17(a),17(b) and 17(c), various frame structures can be configured, and aproposed pilot sequence transmission method is related to an HE-STF(High Efficiency Short Training Field) in a preamble in a framestructure.

Hereinafter, a new sequence obtained by improving the preamble design asdescribed above will be described. In addition, a corresponding sequencegeneration method will also be explained.

First, preconditions for the proposed sequence generation method aredescribed. In the following description, 0₅ means five consecutive 0s,0₇ means seven consecutive 0s, and 0₁₂ means twelve consecutive 0s. Inaddition, C₅₂ means a vector with size of 52 and it can be defined asshown in Equation 1.

Equation 1C ₅₂=√{square root over (1/2)}{0, 0, 0, c1, 0, 0, 0, c2, . . . ,c12}  [Equation 1]

There are four null tones including DC components in the center of 52components included in C₅₂. C₅₂ are composed of twelve coefficientvalues (i.e., c1, c2, . . . , c12), thirty-six (=12*3) “0” values, andfour null tones, and that is, C₅₂ includes a total of the 52 components.In addition, the STF sequence for the 20 MHz bandwidth used in thelegacy VHT system can be reused for the twelve coefficient values c1 toc12.

Hereinafter, sequences for 20, 40, and 80 MHz bandwidths are describedin detail based on the above vector C₅₂.

First, assuming a system where a 256 FFT size is applied, the sequencefor the 20 MHz bandwidth is defined. The sequence for the 20 MHzbandwidth can be defined as shown in Equation 2.

Equation 20₅C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₇   [Equation 2]

The sequence for the 20 MHz bandwidth defined as shown in Equation 2includes a total of 256 tones (i.e., 5+52+12+52+12+52+12+52+7=256).

The sequence for the 40 MHz bandwidth can be defined as shown inEquation 3.

Equation 30₅C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₇   [Equation 3]

The sequence for the 40 MHz bandwidth defined as shown in Equation 3includes a total of 512 tones. In this case, a sequence component (C₅₂0₁₂ C₅₂ 0₁₂ C₅₂ 0₁₂ C₅₂) obtained by eliminating 0₅ and 0₇ from the 20MHz sequence defined according to Equation 2 is located at the left andright sides of the center 0₁₂. That is, the sequence for the 40 MHzbandwidth is defined through sequential arrangement of 0₅—a part of thesequence for 20 MHz-0₁₂—a part of the sequence for 20 MHz-0₇.Alternatively, the sequence for the 40 MHz bandwidth can be defined byrepeating the sequence for the 20 MHz bandwidth twice (0₅+0₇=0₁₂).

The sequence for the 80 MHz bandwidth can be defined as shown inEquation 4.

Equation 40₅C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂. . . . . .0₅C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₁₂C₅₂0₇  [Equation 4]

As shown in Equation 4, the sequence for the 80 MHz bandwidth includes atotal of 1024 tones, and it can be defined by repeating the sequence forthe 20 MHz bandwidth four times (0₅+0₇=0₁₂). In this case, a DCcomponent can be inserted into the center component 0₁₂ of theaforementioned sequences for 20, 40, and 80 MHz.

Hereinafter, a new STF sequence defined by adding specific tones, whichare repeated at an interval of 4 tones or 2 tones, to the 0₁₂ componentis described based on the aforementioned sequence structures. By doingso, when a subband in the new sequence is assigned to a UE, the subbandassigned to the UE can include non-zero values in all cases. Meanwhile,the aforementioned C₅₂ component of the sequences for 20, 40, and 80 MHzcan be identically applied to the conventional STF and LTF sequences.

According to an embodiment, a sequence can be generated by replacing atleast one 0₁₂ component of the sequences defined according to Equation 2to Equation 4 with a D₁₂ component. In this case, the D₁₂ componentmeans a component obtained by substituting the zero values of the O₁₂component with non-zero values repeated at the interval of 4-tone or2-tone. For instance, the D₁₂ component according to the embodiment canbe defined as shown in Equation 5.

Equation 5D ₁₂={0 0 0 1+j 0 0 0−1−j 0 0 0−1−j}  [Equation 5]

In the embodiment according to equation 5, the D₁₂ component includesnon-zero values such as 1+j at the fourth tone, −1−j at the eighth tone,and −1−j at the twelfth tone. In each of the sequences for 20, 40, and80 MHz, at least one 0₁₂ component can be substituted with the D₁₂component in Equation 5.

However, compared to a case where the O₁₂ component is used, such asubstitution process may increase a peak to average power ratio (PAPR).According to an embodiment, a UE/AP can rotate a phase by a unit of{C₁₂D₁₂} and/or {C₁₂} to reduce the PAPR. In other words, a phaserotation factor γ_(k) can be applied to the proposed sequences.

For example, if C₅₂ is the same as that of the STF sequence of the VHTsystem, it can be defined as shown in Equation 6.

Equation 6C ₅₂=√{square root over (1/2)}{0001+j000−1−j000−1−j000−1−j0001+j0000−−000−1−j000−1−j0001+j0001+j0001+j0001+j}  [Equation 6]

In this case, if D₁₂ is applied to the 20 MHz sequence according to theproposed embodiment, a new 20 MHz sequence can be defined as shown inEquation 7.

Equation 7S_(20 MHz)=[0₅C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂0₇]  [Equation 7]

Equation 8 shows a process for applying the phase rotation factor to thesequence in Equation 7.

In Equation 8, a k value of γ_(k) indicates an index of the phaserotation factor applied to each sequence and a superscript character 20indicates that the corresponding phase rotation factor is applied to the20 MHz sequence.

In an embodiment according to Equation 7, a process for determining avalue of the phase rotation factor to optimize the PAPR (=1.7379) isdisclosed. First, Table 2 below shows eight cases of γ_(k) capable ofobtaining the optimum PAPR value corresponding to 1.7379. In Table 2,each column indicates an index of the phase rotation factor (i.e., k=1,2, 3, or 4) and each row indicates one of eight independent cases.

TABLE 2 1 1 1 −1  1 −1  −1  −1  −1  1 1 1 −1  −1  −1  1  1i  1i  1i −1i  1i −1i  −1i  −1i  −1i   1i  1i  1i −1i  −1i  −1i   1i

Meanwhile, if 0₁₂ is used in Table 2 instead of D₁₂ (i.e., the 0₁₂component is set to ‘0’), the PAPR can be decreased, whereby a value of1.6747 can be obtained. Table 3 below shows an example of implementing aphase rotation factor for the 20 MHz sequence when 0₁₂ is used asdescribed above. In this case, there are a total of 32 cases.

TABLE 3 1 1 1 −1  1 1 −1  1 1 −1  1 1 1 −1  −1  −1  1  1i 1 −1i  1  1i−1   1i 1 −1i  1  1i 1 −1i  −1  −1i  −1  1 1 1 −1  1 −1  −1  −1  −1  1−1  −1  −1  −1  1 −1   1i 1  1i −1   1i −1  −1i  −1  −1i  1 −1i  −1 −1i  −1   1i  1i 1  1i −1   1i 1 −1i  1  1i −1   1i 1  1i −1  −1i  −1  1i  1i  1i −1i   1i  1i −1i   1i  1i −1i   1i  1i  1i −1i  −1i  −1i −1i  1  1i 1 −1i  1 −1i  −1  −1i  −1   1i −1  −1i  −1  −1i  1 −1i   1i 1i  1i −1i   1i −1i  −1i  −1i  −1i   1i −1i  −1i  −1i  −1i   1i

Additionally, sequences for 40 and 80 MHz can be created by extendingthe 20 MHz sequence in Equation 7. That is, a sequence for the 40 MHzbandwidth can be generated based on the 20 MHz sequence and a sequencefor the 80 MHz bandwidth can be generated based on the 40 MHz sequence.

Hereinafter, processes for generating the sequences for 40 and 80 MHzand examples of implementing a phase rotation factor for each of thesequences are described. First, the sequence for the 40 MHz bandwidthobtained by extending the sequence for the 20 MHz bandwidth (S_(20 MHz))can be defined as shown in Equation 9.

In Equation 9, S′_(20 MHz) indicates a partial sequence created byeliminating the first component 0₅ and the last component 0₇ from thesequence for the 20 MHz bandwidth, S_(20 MHz). That is, the sequence forthe 40 MHz bandwidth, S_(40 MHz) can be generated by repeating a part ofthe sequence for the 20 MHz bandwidth. Similarly, the sequence for the80 MHz bandwidth, S_(80 MHz) can be defined by extending S′_(40 MHz) asshown in Equation 10. In this case, S′_(40 MHz) indicates a partialsequence created by eliminating the first component 0₅ and the lastcomponent 0₇ from S_(40 MHz).

Table 4 below shows optimum PAPRs of sequences defined for individualbandwidths according to FFT applied to the proposed communication system

Table 4

TABLE 4 BW FFT PAPR 20 MHz 256 1.7379 40 MHz 512 2.2941 80 MHz 10243.5251

Table 5 shows PAPRs according to sequences and FFT defined in theconventional 802.11ac system.

Table 5

TABLE 5 BW FFT PAPR 20 MHz 64 1.6179 40 MHz 128 1.6179 80 MHz 256 1.6747

It can be seen in Tables 4 and 5 that when the proposed sequences areused, corresponding PAPRs are increased. That is, the phase rotationfactor γ_(k) needs to be adjusted to reduce the PAPRs, and thus, anembodiment for setting a value of the phase rotation factor is describedin the following.

First, described is an embodiment of configuring a phase rotation factorfor the sequence for the 40 MHz bandwidth. The phase rotation factor forthe partial sequence S′_(20 MHz) of the sequence for the 20 MHzbandwidth is described with reference to Equation 10. Hereinafter,unlike Equation 9, an embodiment for configuring a phase rotation factorby further segmenting S_(40 MHz) into smaller parts is described.

S_(40 MHz) can be divided into two parts and then represented as shownin Equation 11.

Equation 11S_(40 MHz)=[0₅S_(40 MHz) ¹S_(40 MHz) ²0₇]S_(40 MHz) ¹=[C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂]S_(40 MHz) ²=[C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂]  [Equation 11]

When S_(40 MHz) ¹ and S_(40 MHz) ² are defined as shown in Equation 11,the phase rotation factor can be defined and applied in a unit of{C₁₂D₁₂} as shown in Equation 12.

In other words, similar to Equation 9 where the phase rotation factorfor the sequence for the 20 MHz bandwidth is configured in a unit of{C₁₂D₁₂} and/or {C₁₂}, the phase rotation factor for the sequence forthe 40 MHz bandwidth can be defined in the unit of {C₁₂D₁₂} and/or{C₁₂}. Such an embodiment can be expressed as shown in Equation 12.

When the phase rotation factor for the 40 MHz bandwidth is determined bythe segmentation, the PAPR in Table 4 can be decreased from 2.2941 to2.0227. Table 6 shows eight cases of the phase rotation factor thatsatisfies the condition of PAPR=2.0227. In Table 6, each columnindicates an index of the phase rotation factor (i.e., k=1, 2, . . . ,8) and each row indicates one of the eight independent cases

TABLE 6 1  1i −1  −1  −1   1i 1 −1  1 −1i  −1  −1  −1  −1i  1 −1  −1  1i 1 1 1  1i −1  1 −1  −1i  1 1 1 −1i  −1  1  1i 1 −1i  −1i  −1i  1  1i−1i   1i −1  −1i  −1i  −1i  −1   1i −1i  −1i  1  1i  1i  1i 1 −1i   1i−1i  −1   1i  1i  1i −1  −1i   1i

Meanwhile, in the case of the 40 MHz sequence, if 0₁₂ is used instead ofD₁₂, the PAPR can be decreased to 1.6747. In addition, it is possible toimplement 128 different results according to phase rotation factors. Inother words, a total of 128 different sequences satisfying the conditionof PAPR=1.6747 can be generated and individual phase rotation factorsare given as shown in Table 7.

TABLE 7 1 1 1  1i −1  1 −1   1i 1 1 1 −1i  −1  1 −1  −1i  1 1 −1   1i−1  1 1  1i 1 1 −1  −1i  −1  1 1 −1i  1 1  1i 1 1 −1   1i −1  1 1  1i−1  1 −1   1i 1 1 1 −1i  1 1 −1  −1i  −1  1 1 −1i  −1  1 −1  −1i  1 1−1  1  1i −1  −1  −1   1i 1 −1  1 −1i  −1  −1  −1  −1i  1 −1  −1   1i−1  −1  1  1i 1 −1  −1  −1i  −1  −1  1 −1i  1 −1   1i 1 1 1  1i −1  1−1   1i −1  1 1  1i 1 1 −1  −1i  1 1 1 −1i  −1  1 −1  −1i  −1  1 1 −1i 1 −1  1 1  1i 1 1 −1   1i −1  1 1 −1i  1 1 −1  −1i  −1  1 −1   1i 1 1 1 1i −1  1 −1  −1i  1 1 1 −1i  −1  1  1i 1 −1  −1   1i −1  −1  1  1i −1 −1  −1   1i 1 −1  1 −1i  1 −1  −1  −1i  −1  −1  1 −1i  −1  −1  −1  −1i 1 −1  −1  1  1i 1 −1  −1   1i −1  −1  1 −1i  1 −1  −1  −1i  −1  −1  −1  1i 1 −1  1  1i −1  −1  −1  −1i  1 −1  1 −1i  −1  −1   1i 1 −1  1  1i−1  −1  −1   1i −1  −1  1  1i 1 −1  −1  −1i  1 −1  1 −1i  −1  −1  −1 −1i  −1  −1  1 −1i  1 1  1i 1 1 −1   1i −1  1 1  1i 1 −1  −1   1i −1 −1  1  1i −1  1 −1   1i 1 1 1  1i −1  −1  −1   1i 1 −1  1  1i  1i  1i 1−1i   1i −1i  1  1i  1i −1i  1 −1i   1i  1i 1  1i −1i   1i 1 −1i  −1i −1i  1  1i −1i  −1i  1 −1i  −1i   1i 1 −1i  1 1 −1  −1i  −1  1 1 −1i  1−1  −1  −1i  −1  −1  1 −1i  −1  1 −1  −1i  1 1 1 −1i  −1  −1  −1  −1i  1−1  1 −1i   1i  1i 1  1i  1i −1i  1 −1i   1i −1i  1  1i  1i  1i 1 −1i −1i   1i 1  1i −1i  −1i  1 −1i  −1i  −1i  1  1i −1i   1i −1   1i 1 1 1 1i −1  1 −1   1i 1 −1  1  1i −1  −1  −1   1i −1  1 1  1i 1 1 −1   1i−1  −1  1  1i 1 −1  −1   1i  1i  1i −1  −1i   1i −1i  −1   1i  1i −1i −1  −1i   1i  1i −1   1i −1i   1i −1  −1i  −1i  −1i  −1   1i −1i  −1i −1  −1i  −1i   1i −1  −1i  1 1 1 −1i  −1  1 −1  −1i  1 −1  1 −1i  −1 −1  −1  −1i  −1  1 1 −1i  1 1 −1  −1i  −1  −1  1 −1i  1 −1  −1  −1i   1i 1i −1   1i  1i −1i  −1  −1i   1i −1i  −1   1i  1i  1i −1  −1i  −1i   1i−1   1i −1i  −1i  −1  −1i  −1i  −1i  −1   1i −1i   1i  1i 1 1 1  1i −1 1 −1   1i 1 1 −1   1i −1  1 1  1i 1 −1  1  1i −1  −1  −1   1i 1 −1  −1  1i −1  −1  1  1i 1  1i  1i −1i  1 −1i   1i  1i 1  1i −1i  −1i  1 −1i −1i   1i 1 −1i   1i −1i  1  1i  1i  1i 1 −1i  −1i  −1i  1  1i −1i   1i−1  1 1  1i 1 1 −1   1i −1  1 −1   1i 1 1 1  1i −1  −1  1  1i 1 −1  −1  1i −1  −1  −1   1i 1 −1  1  1i −1   1i  1i −1i  −1  −1i   1i  1i −1  1i −1i  −1i  −1  −1i  −1i   1i −1  −1i   1i −1i  −1   1i  1i  1i −1 −1i  −1i  −1i  −1   1i −1i  −1i  1 1 1 −1i  −1  1 −1  −1i  1 1 −1  −1i −1  1 1 −1i  1 −1  1 −1i  −1  −1  −1  −1i  1 −1  −1  −1i  −1  −1  1 −1i 1  1i  1i  1i 1 −1i   1i −1i  1  1i −1i   1i 1 −1i  −1i  −1i  1 −1i   1i 1i 1  1i  1i −1i  1 −1i  −1i   1i 1  1i −1i  −1i  −1  1 1 −1i  1 1 −1 −1i  −1  1 −1  −1i  1 1 1 −1i  −1  −1  1 −1i  1 −1  −1  −1i  −1  −1  −1 −1i  1 −1  1 −1i  −1   1i  1i  1i −1  −1i   1i −1i  −1   1i −1i   1i −1 −1i  −1i  −1i  −1  −1i   1i  1i −1   1i  1i −1i  −1  −1i  −1i   1i −1  1i −1i   1i  1i 1  1i  1i −1i  1 −1i   1i  1i 1 −1i   1i −1i  1  1i  1i 1i −1   1i  1i −1i  −1  −1i   1i  1i −1  −1i   1i −1i  −1   1i  1i  1i 1i 1 −1i   1i −1i  1  1i  1i  1i −1  −1i   1i −1i  −1   1i  1i −1i  1−1i   1i  1i 1  1i  1i −1i  −1  −1i   1i  1i −1   1i −1i  1  1i  1i  1i1 −1i   1i −1i  1 −1i   1i  1i 1  1i  1i −1i  −1   1i  1i  1i −1  −1i  1i −1i  −1  −1i   1i  1i −1   1i  1i −1i   1i 1 −1i  −1i  −1i  1  1i−1i   1i −1  −1i  −1i  −1i  −1   1i −1i  −1i  1 −1i  −1i   1i 1  1i −1i −1i  −1  −1i  −1i   1i −1  −1i   1i 1  1i −1i  −1i  1 −1i  −1i   1i 1−1i  −1i  −1i  1  1i −1i   1i −1   1i −1i  −1i  −1  −1i  −1i   1i −1 −1i  −1i  −1i  −1   1i −1i   1i  1i 1  1i  1i −1i  1 −1i   1i  1i −1  1i  1i −1i  −1  −1i   1i −1i  1  1i  1i  1i 1 −1i   1i −1i  −1   1i  1i 1i −1  −1i  −1i  1  1i −1i   1i 1 −1i  −1i  −1i  1 −1i  −1i   1i 1  1i−1i  −1i  −1   1i −1i   1i −1  −1i  −1i  −1i  −1  −1i  −1i   1i −1   1i−1i  −1i   1i 1  1i −1i  −1i  1 −1i  −1i   1i −1   1i −1i  −1i  −1  −1i −1i  −1i  1  1i −1i   1i 1 −1i  −1i  −1i  −1   1i −1i   1i −1 

Next, an embodiment for segmenting a phase rotation factor for thesequence for the 80 MHz bandwidth is described. Two differentembodiments can be applied to the sequence for the 80 MHz bandwidth.

As a first method, a sequence for the 20 MHz bandwidth having 256components is first generated, and then a sequence for the 80 MHzbandwidth having 1024 components can be generated by repeating thesequence for the 20 MHz bandwidth four times. The first method can beexpressed as shown in Equation 13.

In Equation 13, a value of γ_(k) is determined based on a directioncapable of minimizing a PAPR of the 80 MHz sequence. In other words, inEquation 14, the phase rotation factor γ_(k) (where k=1, 2, 3, or 4) forthe 20 MHz bandwidth is determined by an optimum value for the 80 MHzsequence rather than an optimum value for the 20 MHz sequence. That is,in Equation 13, the phase rotation factor γ_(k) (where k=5, 6, 7, or 8)is not simply determined in consideration of four times repetition ofthe 20 MHz sequence but is determined based on phase rotation factorsfor the 20 MHz bandwidth and phase rotation factors for the 80 MHzbandwidth.

In the case of the 80 MHz sequence in accordance with the first method,it is possible to obtain a PAPR value equal to 2.1348.

TABLE 8 1 −1 −1 −1  1  1  1 −1 1 −1 −1 −1 −1 −1 −1  1 1 −1 −1 −1   i   i  i  −i 1 −1 −1 −1  −i  −i  −i   i

As a second method for the 80 MHz sequence, a method similar to thesegmentation embodiment for the 40 MHz sequence can be applied. That is,phase rotation factors for the 80 MHz sequence can be determined in theunit of {C₁₂D₁₂} and/or {C₁₂}. The 80 MHz sequence in accordance withthe second method can be expressed as shown in Equation 14.

Equation 14S_(80 MHz)=[0₅S_(80 MHz) ¹S_(80 MHz) ²0₇]  [Equation 14]S_(80 MHz) ¹=[C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₁₂D₁₂C₅₂D₅₂C₅₂D₁₂C₅₂D₁₂]S_(80 MHz) ²=[C₅₂D₁₂C₅₂D₅₂C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₁D₁₂C₅₂]

The 80 MHz sequence can be divided into two parts (S_(80 MHz) ¹,S_(80 MHz) ²) as shown in Equation 14. Each of the two parts includes 8{C₁₂D₁₂} components, i.e., the 80 MHz sequence includes a total of 16{C₁₂D₁₂} components (the last 16^(th) component includes only C₁₂).Accordingly, since the phase rotation factor is applied in the unit of{C₁₂D₁₂}, a total of 16 phase rotation factor values can be defined fora single sequence. This can be expressed as shown in Equation 15 and theoptimum PAPR can be achieved through Equation 15.

$\begin{matrix}{\mspace{79mu}{{Equation}\mspace{14mu} 15}} & \; \\{{S_{80\mspace{11mu}{MHz}}^{1} = \left\lbrack {\frac{C_{52\;}\mspace{11mu} D_{12}}{\begin{matrix} \times \\\gamma_{1}\end{matrix}}\frac{C_{52\;}\mspace{11mu} D_{12}}{\begin{matrix} \times \\\gamma_{2}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{3}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{4}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{5}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{6}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{7}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{8}\end{matrix}}} \right\rbrack}{S_{80\mspace{11mu}{MHz}}^{2} = \left\lbrack {\frac{C_{52\;}\mspace{11mu} D_{12}}{\begin{matrix} \times \\\gamma_{9}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{10}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{11}\end{matrix}}\frac{C_{52\;}\mspace{11mu} D_{12}}{\begin{matrix} \times \\\gamma_{12}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{13}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{14}\end{matrix}}\frac{C_{52}\mspace{14mu} D_{12}}{\begin{matrix} \times \\\gamma_{15}\end{matrix}}\frac{C_{52}}{\begin{matrix} \times \\\gamma_{16}\end{matrix}}} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

If D₁₂ is equal to 0₁₂ in Equation 15, 6144 phase rotation factorssatisfying the condition of PAPR=1.6747 can be generated and each of thephase rotation factors includes 16 components (γ={γ₁, γ₂, . . . γ₁₆}).

Table 9 below shows 704 sequences corresponding to baseline sequencesamong the 6144 phase rotation factors. In Table 9, there are a total of704 rows and each of the rows indicates a baseline sequence composed of16 components. In addition, Table 9 shows each block by dividing the 704rows into a random number to easily distinguish between the individualsequences.

TABLE 9 1 1 1  1 1 −1   −i  i 1 1 −1 −1   1 −1 i  −i 1 1 1  1 1 −i    i−1   1 −1 −1 1 1  i −i   −1 1 1 1  1  i 1  i −1   −1 1 −1 1 −i    i i −11 1 1  1  i −i   −1    1 −1 −1 1 1 −i    1 −1    1 1 1 1 −1 1 −1   −i −i1 1 −1 1 1 −1 i  i 1 1 1 −1 1 1 −i −i 1 1 −1 1 −1    1 i  i 1 1 1 −1 −1  −i    i −1   1 −1 −1 −1   −1    i −i   −1 1 1 1 −1  i −1   −i −1   −11 −1 −1   −i   −1 i −1 1 1 1 −1 −i   −1    i −1   −1 1 −1 −1    i −1 −i  −1 1 1 1  i 1  i −i −i 1 −1 −1  i 1 −1 i  −i 1 1 1  i −1   1 −i −1   11 −1 −1   −1    1 1    1 1 1 1  i −1   −i    i  i 1 −1 −1  i −1    1 −i   i 1 1 1  i  i −1   −i  i −1 1 −1  i −i   −1 i  i 1 1 1  i −i   1  i−i −1 1 −1  i 1  1 −i    −i 1 1 1  i −1    i −1    i −1 −1 1  i  i −1 −1   i 1 1 1  −i 1  i −i  i 1 −1 −1 −i    i −1 i  i 1 1 1 −1 −1   1 −i  11 1 −1  i −1    1 1   −1 1 1 1 −1 −1   −i    i −i 1 −1 −1 −i   −1    1−1    −i 1 1 1  −i  i −1   −i −i −1 1 −1 −i   −i   −1 i  −i 1 1 1  −i −i  1  i  i −1 1 −1 −i    i  1 −i    i 1 1 1 −1 −1    i −1   −i −1 −1 1 −i   i −1 −1    −i 1 1 −1  1 1  i  i −1   1 −1 1 1 1  −i −1   −1 1 1 1 1 1 i −i −1 1 −1 −1  1 1 −i i −1 1 1 1 1 −1    i  i  i 1 1 −1 −1 −1    1 i −i 1 1 1 1  i −1   −i  1 −1 1 −1  1 −i   −1   i  1 1 1 1 1 −i    1  i−1 −1 1 −1  1  i  1 −i   −1 1 1 1 −1   1  i −i  1 1 −1 −1 −1 1 −i i  1 11 1 −1   −1    i −i −1 1 −1 −1 −1 −1   −i i −1 1 1 1 −1    i  1 −1    1−1 1 −1 −1 −1   −1   1    1 1 1 1 −1    i −i −1   −1 −1 −1 1 −1 −i    i−1   −1 1 1 1 −1   −i    i −1   −1 −1 −1 1 −1  i −i −1   −1 1 1 1 1 1 −i 1  −i 1 −1 −1  i 1  i −i    −i 1 1 1  i −1    i −i  1 1 −1 −1  i −1  −i i  1 1 1 1 1  i  1 −1   −1 −1 1 −1  i −i    1 1   −1 1 1 1  i  i −i−1    i −1 −1 1  i −i    i −1    i 1 1 1  i −i   −1    i  i −1 1 −1  i i −i −i    i 1 1 1 −i   1 −1   −i  1 1 1 −1  i 1 −1   i −1 1 1 1 −i   1−i  i  i 1 −1 −1  −i 1  i −i    i 1 1 1 −i   −1    i −i  −i 1 −1 −1  −i−1   −i i  −i 1 1 1 −i    i  1 −i  i −1 1 −1  −i −i    1 i  i 1 1 1 −i   i −i −1    −i −1 −1 1  −i −i    i −1    −i 1 1 1 −i   −i   −i  i  −i −11 −1  −i  i −i −i    −i 1 1 −1 1 1 −1   −1    −i 1 1 1 −1 1 −1   i  i 11 −1 1 1 −i −1   −1 1 −1 1  1 1  i i −1 1 1 −1 1 −1  1 −i  −i 1 1 1 −1−1 1 i i 1 1 −1 1  i  1  1 −1 −1 1 1  1  −i 1 −i   −1   1 1 −1 1  1 −i−1   −1 −1 −1 −1    1  −i 1 −1   −1   1 1 −1 1  −i −1   −i  1 −1 1 1  1 i −1   i 1   1 1 −1 −1    1 −1   −i  i 1 1 1  1  1 −1   i −i   1 1 −1−1   −1  1 −i  i 1 1 1  1 −1 1 i −i   1 1 −1 −1   −1 −i −i −1 1 −1 1 −1−1  i i −1   1 1 −1 −1    i −i −1    1 −1 −1 −1   −1 −1 1 −1   1   1 1−1 −1    −i −1   −i −1 −1 1 1 −1  i −1   i −1   1 1 −1  i  1 −1   −i  11 1 1  −i  1 −1   i −1   1 1 −1  i  1 −i −i  −i 1 −1 1  i  1 1 i −i   11 −1  i −1  i  i  i 1 −1 1  i −1 −i   −i   i 1 1 −1  i  i  1  i  −i −1 11  i  −i 1 −i   −i   1 1 −1  i  i −i −1    −i −1 −1 −1    i  −i  i −1  −i   1 1 −1  i  −i  i  1  i −1 −1 −1    i  i −i   1   i 1 1 −1 −i    1 i  1 −1 1 −1 −1    i  1 −i   1   1   1 1 −1 −i   −1  1  i  1 1 1 1  i−1 1 −i   −1   1 1 −1 −i   −1 −i −1    1 1 −1 −1    i −1  i −1   −1   11 −1 −i    i −1    i −1 −1 1 1  −i  −i −1   −i   −i   1 1 −1 −i    −i  1−i  i −1 1 1  −i  i 1 i i 1 1 −1 −i    −i  i −1    i −1 −1 −1    −i  i−i   −1   i 1 1  i 1  1  i −i  −i 1 −1  i −1  1 −i   −i   i 1 1  i 1 −1 1 −1   −1 1 1 −i   −1 −1 1 1   i 1 1  i 1 −1 −i  i  i 1 −1  i −1 −1  ii −i   1 1  i 1  i −1    i  −i −1 1  i −1  −i −1   i i 1 1 −1 1 −1    −i−i 1 1 −1 1  1 −1    i  i 1 1 1 −1 1 i −1  i 1 −1 1 1  1 −1   −1 −1   11 1 −1 1 −i    1 −i −1   −1 1 1  1  i  1  i −1   1 1 −1 1 −i    i −1  −1   −1 −1 −1    1  i  −i −1   −1   1 1 −1 −1   1   −1 −i 1 1 −1 1 −1 1 i  i 1 1 1 −1 −1   −1    i  i −1   1 −1 1 −1 −1    −i −i −1   1 1 −1 −1  i −1  i −1   −1 1 1 −1 −i   −1 −i −1   1 1 −1 −1   −i    1 −i 1 −1 1 1−1  i  1  i 1 1 1 −1 −1   −i    i −1   1 −1 −1 −1   −1  i  −i −1   1 1 1−1  i 1    i  i −i   1 −1 1  i  i  −i −i −i   1 1 −1  i −1    1 −i 1 1 11  −i −1    1  i −1   1 1 −1  i −1    −i −i  i 1 −1 1  i −1    i  i  i 11 −1  i i −1  i  i −1 1 1  i −i   −1 −i  i 1 1 −1  i −i   −1 −1   −1  −1 1 −1    −i 1 −1 −1   1 1 1 −1 −i   1   −1  i 1 1 1 1  i 1 −1 −i −1  1 1 −1 −i   1    −i  i 1 1 −1 −1    i 1  i  1 −1   1 1 −1 −i   −1    i−1   −1   1 −1 −1    i −1    −i −1   1 1 1 −1 −i   i  i  i  i −1 1 1  −i−i    1 −i  i 1 1 −1 −i   i  −i −1    i −1 −1 −1    −i −i    i −1   1 11 −1 −i   −i   −1 −i −i   −1 1 1  −i 1 −1  i −1   1 1  i 1 1   −1 −1  −i   1 1 −i   −1 1 −1  1  i 1 1  i 1 1    −i −i  i 1 −1  i −1 1  i −i −i  1 1  i 1 −1    i  i −i   1 −1  i −1 −1    −i  i  i 1 1  i 1 i  1 −i −i  −1 1  i −1 −i    1 −i  i 1 1  i 1 i  −i −i 1 −1 −1  i  1 −i    i −i 11 1 i 1   −i    1 −i    i −1 1  i −1    i  1  −i −i 1 1 1   −1   1 −1 1−i 1 1 −i 1  1 −1 −1  i 1 1 i −1   −1    1 −1    i 1 1 −i 1 −1  1  1 −i1 1 i −1   −1    −i  i −i 1 −1  i 1 −1  i  i  i 1 1 1   −1   1 −1  i  1−1 1  i 1 −1 −1  i −i 1 1 i −1   −i   −1 −1   −1   −1 1 −i −1    i −1  1−1   1 1 i i 1  i 1 −i 1 −1 −i  i  1  −i −1 −i 1 1 i i −1    1 1 −1   11 −i −i   −1  1 −1  1 1 1 i i −1    −i −1    i 1 −1 −1    i −1  i  1  i1 1 i i  i −1 1  i −1 1 −i  i  −i −1 −1  i 1 1 1   i −i    1 −1   −i −11 −i  i  i  1  1 −i 1 1 i i −i    i  i −i −1 −1  i  i  i  −i  i −i 1 1 i−i   1  i −i   −1   1 −1  i  i  1  −i  −i  1 1 1 1   −i   −1    i 1 −i 1−1 −i −i   −1  −i −1 −i 1 1 i −i    i  1 1  i −1 1 −i −i    −i  1 −1  i1 1 i −i    i  −i  i  i −1 −1  i −i    −i  i  i  i 1 1 1   −i   −i   −1−1   −i −1 1 −i −i    1 −1  1 −i 1 1 −i   1   1 −1 1 −i 1 1  i −1    1−1 −1  i 1 1 −1   1   1  −i 1 −1   1 −1  i 1  1  1 −1 −1   1 1 −i   1  −1    i −1    1 1 −1  i 1 −1  −i  1  1 1 1 −i   1    i −1 −1    1 −1 1 i 1  −i −1  1  1 1 1 i  1 −i  i  i −1   −1 −1 i 1 i −i    i −1   1 1 i−1    1 −i   −i   −i 1 −1 i 1 i  i −i    i 1 1 i −1   −1    i  i  i 1 −1i 1 −1   −i    i −i 1 1 i −1    i 1 −i    i −1 1 i 1 −i   1 −i   −i 1 1i −1    i −i   −i   −1   −1 −1 i −1   −1    i −i   −1   1 1 i −1   −i  i i  1 −1 −1 i −1   i −i    i  1 1 1 i  i  1 −i   −1   −i 1 −1 −i    i 1   i 1 −i 1 1 i  i −1    i 1  i 1 −1 −i   1 −1   −i   −1    i 1 1 i  i i 1 1 −i −1 1 −i    i −i   1 −1   −i 1 1 i  i  i −i    i −i −1 −1 i  i−i    i  i −i 1 1 i  i −i −1   −1    i −1 1 −i    i i −1   1  i 1 1 i −i 1 −1   1  1 1 1 −i    i 1   −1   −1   −1   1 1 i −i  1 −i   −i    1 1−1 i  i 1    i −i   −1   1 1 i −i −1   −i   −1   −i 1 −1 −i   −i   −1   i 1 −i 1 1 i −i  i −1   1 −i −1 1 −i   −i   −i   −1   −1   −i 1 1 i −i−i 1 −1    i −1 1 −i   −i   i 1 1  i 1 1 i −i −i  i  i  i −1 −1 i −i   i−i    i  i 1 1 −i    1  1  i −1   −1   1 −1 i 1 1   −i   1 −1   1 1 −i   1 −1   1 1 −1   1 1 i −1   −1   1 −1    i 1 1 −i    1  i 1 −1   −1   −11 i 1 −i   1 1 −1   1 1 −i    1 −i 1 1 −1   −1 1 i 1 i 1 −1   −1   1 1−i  1 −i −1   1 1 −1 1  i 1 i −1 −1  1 1 1 −i −1  1 −1   1  i 1 1  i 1 1  −1 −1 −i 1 1 −i −1 −1   1 1  i 1 1  i 1 −1    1 −1 −i 1 1 −i −1 −1  −i   1 −1   1 −1  i −1   −1    i −1 −1   1 1 −i −1  i −1   −i    i −1 1−i 1 −i   −1  −i −i 1 1 −i −1 −i 1  i −i   −1 1 −i 1 i  1  i  i 1 1 −i−1 −i 1 −i   1 −1 −1 −i −1   i −1  −i  1 1 1 −i  i  1 −i   1 −i   1 −1 i  i 1    i −1 −i 1 1 −i  i −1    i −i   1 1 −1 −i −i   −1    −i  −i −1  1 1 −i  i  1 −1   −i   1 −1 1 −i −i   −i   −1  −i −1   1 1 −i  i −i 1 i −1   −1 1 −i −i   i  1  i  1 1 1 −i  1 −i   1  i 1 −1 −1 −i 1  i −i 11 1 1 −i −1 1   1 −1   1 1 −1  i −1    1 −i 1 1 1 1 −i −1 −1    i −1  −1   1 −1  i −1   −1   −i 1 −1   1 1 −i −1 i 1  i  i −1 1 −i 1 −i  1  i−i   1 1 −i −1 i −i   −i 1 −1 −1 −i −1   −i  i −i   1 1 1 −i −1 −i   −1  −i −i   −1 1 −i 1  i −1   −i    i 1 1 −i  i 1   1 −1   −i   1 −1  i 1 1 −i 1 −1   1 1 −i  i −1   1  1 1 1 1  i −i   −1    1 −1   −1   1 1 −i i i 1  i 1 −1 1 −i −i   −i  1  i −1   1 1 −i  i i −i   −i −i   −1 −1 −i1 −i  i −i   −i   1 1 −i  i −i   −1   −i −1   −1 1 −i −i    i −1   −i  1 1 1 −i   −i   −1 −1   −1   1 1 −1  −i  i −1    i −1   −1 1 1 −i   −i   i −1   −1   −1   −1 1  −i  i −i   −1   −i   1 1 1 −i   −i    −i 1  1 1−1 1 −1 1  i 1 i −1 1 1 −i   −i    −i  i −1    i −1 −1  −i −1    i −i  −i   1 1 −1 1 1  1  i  i −1   1 1 −1 1 1 −1   −i   −1 1 −1 1 1 −1 −1  −i  i 1 −1 −1 −1   −1   −1   i −1 1 −1 1 1 −1 −i   −i 1 1 1 −1 1 −1    ii 1 1 −1 1 1  i −1   −i −1   −1 −1 −1 1 −i   −1   i −1 1 −1 1 1  −i −1   i −1   −1 −1 −1 1  i −1   −i   −1 1 −1 1 −1    1 1 −i −i   1 −1 −1 1 11 i 1 1 −1 1 −1    1 −1   −i 1 1 1 −1 −1   1  i 1   1 1 −1 1 −1   −1 1 i −1   1 1 −1 −1   −1   −i   −i   −1 1 −1 1 −1    i 1 −i −1   −1 −1 −1−1   −i   1 i −1 1 −1 1 −1   −1 1  1 −1   −1 −1  1 1  i 1 1   1 1 −1 1−1    −i −i    1 1 −1 1  1 −1   1 1 1   1 1 −1 1  i  1 −i   −1   1 1 1 1 −1   1 1 −1   −1 1 −1 1  i −1 1  i 1 1 1 −1 1 −1   −1   −i   1 1 −1 11  i 1 −i 1 −1 −1 −1 1 −1   1 i 1 1 −1 1 1  i 1 −1   1 −1 1  1 1 −i   −i  −1   1 1 −1 1 1  −i −1    1 −i   −1 1  1 1 1 1 1   −1 1 −1 1 −i    1 i −1   1 1 1  1 1 1 −i   −1   −1 1 1 −i −i    i  1  i −1   −1 1 −i 1 −1  1  1 1 1 1 −i −i   1  −i −i 1 −1 −1 −i −i   −i    i −1  i 1 1 −1 −1  −i   −1 −1   1 −1 1 −1 1 1 −1   −1 −1   1 −1 1 1 1  1 −i  i 1 −1 −1 −1  1 1  i −i   1 −1 1 1 1  −i −1   −1   1 1 −1 1 1 1  1 −1   1 −1 1 1 −1   i  i 1 1 1 −1 1 −i   −i    −i 1 1 −1 1 1  i  1 −1   1 −1 −1 −1 1 −i   1 1 1 1 −1 1 1 −i    1  i 1 −1 −1 −1 1 1 1  −i 1 1 −1 1 1 −i    −i −1   1−1 1 1 1 1  i −1 1 1 −1 1 −1   1  i  i 1 1 1 −1 −1   1 −i    −i 1 1 −1 1−1   −1   −1 −i −i   1 −1 −1 1 −1   −1    1  i 1 −1 1 −1   −1   −1 −i −1  1 1 −1 −1   −1   1  1 −i   1 −1 1 −1    i −1 −i 1 −1 −1 −1 −1   −i  −1    i 1 1 −1 1 −1   −i   −1 −1   −i   −1 −1 1 1 1 −1   −1  i 1 −1 1  i1  1  i 1 1 −1 −1 −i   1 1  −i −1   1 −1 1  i −1   −1  i 1 1 −1 −1 −i  −1   −1    −i −1   1 −1 1  i −1    −i −i  i 1 1 −1  i −1    i  1  i 1 −11  i  i −1 −i −i   −1 −1 −1  i −i   −1    i −i   1 −1 1  i −i   −1 −1  −1   −1 −1 1 −i   1 −1   −1 1 1 −1 1 −i   1  1  i −1   1 −1 −1  i 1 1 −11 1 −1 1 −i   1 −1 −1   −1   1 1 1 1 1 1 −1 1 1 −1 1  −i −1 −1    i −1  1 −1 −1  1 −1   −1   −1    1 1 −1 1  −i −1 −1   −i   −i   1 1 −1 −i −1   i  i  −i 1 −1 1 −1 −1 1 1 1 −1 −1 1  i 1 1 1 −1 1 −1 1 −1 −1 −i   1 1−1 1 1 −1   1  i 1  1 1 −1 −1  1  1 1 1 1 1 1 −1 −1   1 −i   1  −i 1 −1−1  1 −1 −1   1 1 1 −1 1 −1   −1   −1   −1    −i 1 −1 −1  1 −1 −1   −1  −i   1 1 −1 −1   −1   1 −1    i 1 −1 −1  1  i −1   1 −1   −1 −1 −1 −1  −1   −1   1  i 1 −1 −1  1  −i 1 −i   1 −1 −1 1  1 1 1 1  1 1 −1 −1  1 −i −i   −1   −1   −1 1 −1  1  i 1 −1   −1 1 −1 −1 −1  1 1 1 −1   1 1 −1 1 1 −i   1  i 1 −1 −1 −1 −1 −1    i −1   1 −1 1  1 −1   −1   −i   i 1−1 −1 −1 −1 −i   −1    i 1 1 −1  1 −1    i −i    −i 1 −1 −1 −1  1 −1   11 −1 −1 −1  1 −i   −1   1 −1 1 −1 −1 −1 −1 1 −1   −i   −1 −1 −1  1 1 1−1    i 1 −1 −1 −1  −i −i   1 −1   −1 1 −1 −1    i  i 1 −1 1 −1 −1  1  i−i   1 1 1 1 −1 −i 1  i 1 −1 1 −1 −1  i −1  i −1   −1   1 1 −1 −i −1  −i   −1    1 1 −1 −1  i  i 1 −1   1 −1 −1 −1 −i −1   1 −1   −1 1 −1 −1 i  1  i 1  i −1 1 −1  i −i   −i   1  1 1 −1 −1  i  −i −1   1 −1   −1 −1−1 −i 1 −1   1  1 1 −1 −1  −i  1 1  i 1 1 −1 1  i 1 1 −1   −1 1 −1 −1 −i  1 −i    i  i 1 1 1 −i 1  i −1    i 1 −1 −1  −i −1  i −i   −i   1 11 −i −i   −i    i  −i 1 −1 −1  −i  1 1  i −1   −1 −1 1 −i −i   1 −1   −11 −1 1 −1 −1    1 1  1 1 1 1  i −1 −i 1 −1 1 −1 1  −i i  i 1  i −1 1 1−i −1 −i 1  i 1 −1 1  −i −i   −1 −1    1 −1 −1 1  i  i −1   −1   −1 1 −1−1  1 1    1 1  i 1 −1 1 −1    1  1 −1   −1 1 −1 −1  1 1   −1 1 −1 1 1−1 −1    1  1 1  1 1 −1 −1  1 −1    1 −1    i 1 1 −1 −1   −1 −1   −1   −i 1 −1 −1  1 i  1 −1    −i −1 −1 −1 −1    −i  1 −1    i 1 −1 −1  1 i i −1   −1 −1 1 −1  1  −i −i −1   −1 1 −1 −1  1 −i   −1 1 −1 −1 −1 1  1 i −1   1 −1 1 −1 −1 −1 1    1 1  −i 1 −1 1  1  1  1 −1    i 1 −1 −1 −11   −1 −1    i 1 1 −1  1  i  i 1  −i 1 −1 −1 −1 −1    i −1    −i 1 1 −1 1 −1 −i −1    i 1 −1 −1 −1 i  1 1  i −1 −1 −1  1  −i  1 −1    −i 1 −1−1 −1 i  i 1 −1 −1 1 −1 −1    −i −i 1 −1 1 −1 −1 −1 −i   −1 1  −i −1 −1−1  1  1 −1   1  1 1 −1 −1  i 1    i 1 −1 1 1 −1 −i  1 −i  i  1 1 −1 −1 i −1   −1  i −1 1 −1 1 −i  −i −1   −i    1 1 −1 −1  1 −1   −1 −1    1 11 −1 −1   −1  1 −1   −1 1 −1 −1  i i −1 1  1 −1 −1 −1 −i −1 −1   1 −1 1−1 −1  i −i    i −1   −1 −1 −1 −1 −i  1  1 −1    1 1 −1 −1  i −i   −1  i i −1 1 −1  i  i  i 1  i 1 −1 −1  −i i  i 1  i 1 1 −1  i  i −i 1 −1 1 −1−1 −1 −1   −1 −1   −1 1 −1 1  i −1 −1   1  1 1 −1 −1  −i −1   −1 1  −i 11 1 −i −1  i −1    −i 1 −1 −1  −i i  −i  i  i −1 −1 1 −i  −i −i −i    i1 −1 −1   −i    i  i −1    1 −1 1 −1    −i  −i −i   −1    i 1 −1 −1   −1  −i   −1   −i  1 −1 −1 1    −i  i −1   1  i 1 −1 i 1 1 1 −1    −i 1 −1−i   −1  1 1 1  i 1 −1 i 1 1 −i   −i −1 1 1 i −1  1  i −i    i 1 −1 i 1−1    i  i  1 1 1 1   −1 −1 −i    i  −i 1 −1 i 1  i 1  1  1 −1 −1 −i   1 −1 1 −1    1 1 −1 i 1  i  i  i −1 −1 1 1    1 −1 −i    i −1 1 −1 i  i−i   −1   −i  1 −1 −1 i −1  i −1   −i    −i 1 −1 i −1   1 1 −i  1 1 −1−i    1  1 1 1  −i 1 −1 i −1   1 −i    1  1 1 1 −i   −1  1  i −1    1 1−1 i −1   −1    i −1   −1 1 1 −i   −1 −1 −i   1 −1 1 −1 i −i    i 1  1−1 −1 −1 −1   −1 −1 1 −1   −1 1 −1 i −1    i 1 −i −1 −1 1 i −1  −i −i  −1   −1 1 −1 i  i 1 1  1 −1 1 −1 −i    −i  1 1 −1    1 1 −1 i 1 1 −1   1 −1 1 1 −1    1  1 1 −1   −1 1 −1 i 1 −1   −1    i  1 1 1 i  −i −1  i1 −1 1 −1 i 1  i −1   −i  1 −1 −1 i −1 −1 −1   −1   −1 1 −1 i 1 −i   1 i −1 −1 −1 i  −i  i 1  i  1 1 −1 i −i   1 1 −1   −1 1 −1 −1    i  1 1 1 1 1 −1 i −1   −1   −1   −1   −1 1 −1 −i    1 −1 −1   1  1 1 −1 i −i   11  i −1 −1 −1 i  i  −i 1 1  1 1 −1 i −1   −i   1  i  1 −1 −1 i  i  i 1 i −1 1 −1 i −i   −i   −1   −i −1 −1 1 i  −i  i  i −1    −i 1 −1 −1   11 1  i  i 1 1 −i   −1  1 −1    i  −i 1 −1 −i   1 −1   −1   −1    1 1 −1i −1 −1 −1   1  −i 1 −1 −1   −i   −i   1    −i −i   −1 −1 1    −i  i  1 i −i 1 −1 −1   −i   −i   −i   −1  i −1 1 −1    −i  i  i −1    i 1 −1 i1 1 i −1  i 1 1 i −1  1  −i −i −i 1 −1 i 1 −1   −1   −1 −1   1 −1 −i  −1 −1 −1  1  i 1 −1 i 1 −1   −i    1 1 1 1 −i    1 −1  i −1    1 1 −1 i1 1 −1    1 −1   −1 −1 −i    1 −1 −1 −1   −1   1 −1 i 1 −1   1    i 1 −1−1 i −1  1  1  i −i 1 −1 i 1 −1   −i   −1 1 −1 1 1    1  1  i −i  1 1 −1i −1   1 i −1 −i   1 1 1    1  1  −i −i  i 1 −1 i −1   −1   −1    1 −i  1 −1 −i    1 −1 −1 −1    1 1 −1 i −1   −1   −i    1 −1   1 1 −i   −1 −1 i −1   −1   1 −1 i −1   1 −1   −1  i −1 −1 i  1 −1 −1 −i −1   1 −1 i −1  −i   1    1 −1   −1 −1 i  1  i  1  i  i 1 −1 i  i 1 i −1 −1   1 1 −i   i  1  −i  1 −i 1 −1 i  i −1   −1   −1 1 1 −1 −i   −1 −1 −1  1 −1   1 −1i  i 1 1    1 1 −1 −1 i −1 −1  1  i −i 1 −1 i  i 1 1   −1 1 −1 1 1    1 −i −1 −i  i 1 −1 i  i −i   −i   −1 1 −1 1 i  i  i  i −i  i 1 −1 i −i  1 i −1  i 1 1 i  i  1  −i −i −1   1 −1 i −i   −1   i  1 1 1 1 i  i −1 −i  i −1   1 −1 i −i   1 i −i  −i   −1 1 i  −i  −i  −i −i −i 1 −1 i −1  −i   −i    −i 1 −1 −1 i  i  1 −1 −i −1   1 −1 −i   1 1 1   −1  i 1 −1i −1  1  1  1 −i 1 −1 −i   1 1 −1    1 −1   1 1 −i   −1  1  i  i  i 1 −1−1   1 −1   i −1 1 1 1 −1   −1 −1 −1 −i −i 1 −1 −i 1 −1 −1   −1   −i 1 1−i −1 −1  i −i    i 1 −1 −i 1  i −1   i −i −1 −1 −i −1  −i −1   i  i 1−1 −i 1  −i 1   −i    i −1 −1 −i −1  i  1 −i   −1 1 −1 −i 1 −1 −i   i  1−1 1 −i 1  i  i i  1 1 −1 −i −1  1 i i −i 1 1 −i 1  1 −i i  i 1 −1 −i −1−1 i 1   −1   1 1  i −1 −1 −i −1   −1 1 −1 −i −1  i 1   −1   −1   −1 −1 1 −1  −i  1 1   −1 1 −1 −i −1  1 i i −1   −1 1 −1   −1 −1 −i 1   −1 1−1 −1   1 i 1 −i   −1 −1 −1 −i   −i   −1  1 −i  i 1 −1 −1   1 i 1 −i  −1 −1 1 −i   1  −i −1 −i −1 1 −1 −i 1 −i   −1   1 −1 −1 −1 i 1  i −1 −1  −1 1 −1 −i −1 1   1 1  i 1 −1 i 1  1  1 −i  −i 1 −1 −i −1 −1   −1   1 i 1 −1 i 1 −1 −1 −1   −1 1 −1 −i −1 −1   −i   −1   −1 1 1 i −1   −1  i 1 −1 1 −1 −i −1 i −i   −1    1 −1 −1 i −1    −i −1  1  1 1 −1 −1   −1−i   1 1 −1 −1 −1 i −1    1  1 −1   −1 1 −1   −i    i  1 −i  1 1 1 1 −i−i  1  i  i −1 1 −1   −i    i −1 −i −1   1 1 1 −i −i −1  i −i −1 1 −1  −i    i  i −1    i 1 −1 −1   −i −i  −i −1    i −1 1 −1   −i    i  −i  1−i −1   −1 −1   −i −i  i 1 −i  1 1 −1   −i    i  −i −i −i −i   −1 1 −i i  i  i −i −1 1 −1   −i   −i    1  i  i  i 1 1  i −i  1 −i   −1    i 1−1   −i   −i   −1 −1   −1   1 1 −1    i  i −1 −1    1 −1 1 −1   −i   −i  −1 −i −i −1   1 1 −i  i −1  i −i  1 1 −1   −i   −i    −i  1 −i 1 −1 −1  −i  i  i 1 −i −1 1 −1   −i   −i   −1 −1   −1   1 −1 1 −1   −1    1 1−1    1 1 i 1 1  1 −1   −1   −1   1 −i   −1    1  1 1  i −1 1 i 1 1 −1 1  1 1 1 −i   −1    1 −1 −1   −i  1 1 i 1 1 −1  i −i  i 1  i −1   −1  −1  i  i  −i 1 i 1 1  i −i  1 −i   −1  i  1 −1    −i −i    1  i 1 i 1 1 −i  i  i −1   −1  i −1    1  i  i −i −1 1 i 1 −1    1 −i −i −i   1  i−1    1  1 −i    i  i 1 i 1 −1   −1 −1   −i −1   1 −i   −1   −1   −1 1 i −1 1 i 1 −1    i  i −1    i −1  i  1  1  −i  i −1    −i 1 i 1 −1   −i −1    1 1 −1 −1    1 −1    i 1  1  1 1 i 1 −1    −i −i  1 −i   −1  i 1  1  i −i    1  i 1 i 1 1  1 −1   −1   1 1 −i    1 −1    1 1 −1   −1 1i 1  i −1  1  1 −1   1 −i    1 −i −1 −1    1  1 1 −1   −1   i −1   −1 −1  −1   1 −1    i −i −1   −1 1  1 1 −1   −i   i  i  1 −i 1 −1 −1    −i −i−i    1 −i   −1 1 −1   −i   i  i  i −i −i   −1  1  −i  i −i    −i −i   −i 1 −1   −i   i −i   −1  i −1   −1 −1    −i −i  i −1  i  1 1 −1   −i  −i   1  1 −1   1 1 −1    i  i 1  1 1 −1 1 −1   −i   −i   1  −i −1    i 1 1  i −i 1  1 1  i 1 −1   −i   −1   −1    i −i 1 1  1  −i  i −1   −1 −i  −1 1 −1   −i   −i    i  i −i  i −1  1  −i −i −i    −i −1    1 1 −1  −i   −i   −i   −1  i 1 −1 −1    −i  i  i −1  i −1 1 i 1 1   1  1  i −1  1 −i −1  1 1 −1 −i   −1 1 i 1 1   1 −1 −i 1 1  1 −1 −1   1  −i 1  −i 1 i1 1   −1   −1 −i 1 1 −i −1  1 −1    1  i  1 1 i 1 1    i  i −1   −i   −1 i  1 −1   −i    i −1    i 1 i 1 1   −i   −1  1 −1   −1 −i  1  1  i  1 1−1 1 i 1 −1   1 −1 −i 1 1 −i −1 −1   1  1 1  1 1 i 1 −1   −1    1  i −1  1 −i −1 −1   −1   −1 −i   −1 1 i 1 −1   −1    i −i −i   1  i −1  1 −1   i  i  i 1 i 1 −1    i  −i  1  i −1  i  1  1 −i    −i 1  −i 1 i 1 −1  −1    i −1   −i   −1  i  1  1  i  i −1    i 1 i 1 i 1  1 −1   −1   1 −i 1 −i 1 −1 −1    1 1 i 1 i 1  −i  i 1 1  i −1 −i 1  −i −i   −1 1 i 1 i−1   −1  1 1 1 −i  1 −i −1    i 1 −1 1 i 1  i −1    1  i  1 1 i −1  −i−1 i −1   −1 1 i 1  i  i  1 −1    1 −1 i 1  −i  −i i −1   −1 1 i 1  i −i−1 1 −1 −1 −1   1  i  i 1   1  −i 1 i 1  i −i  −i 1 −1 −1 i 1  −i  i −i  1  1 1 i 1 −i  1 −1 −1   −1 1 −i   1  i  1 1   −1    i 1 i 1 −i −1   1 1  1 1 −i   1  i −1 −1   1 −1 1 i 1 −i −1    i  i −1 1 i −1  i −1 i−i    1 1 i 1 −i  i  i −1   −1 −1 i 1  i  −i i −1    1 1 i 1 −i −i −1 1 i −1 −i   1  −i  i 1   1  i 1 i 1 −i −i −1 1  1 −1 i 1  i  i −i   1 −11 i −1  1  1 −1 1  −i 1 −i   −1 −1  1 1   1  i 1 i −1  1 −1    1 −1    i1 −i   −1 −1 −1 −1   −1    −i 1 i −1  1 −1    i  i  i 1 i 1 −1 −1 i −i   −i 1 i −1  1  i  i  i −1 −1 i 1  1  −i i −i   −1 1 i −1  1 −i −1 −1  −1 −1 −i   −1  1  i 1   −1   −1 1 i −1  1 −i  −i −1    i −1 i −1 −1  i−i   −1    −i 1 i −1 −1    1 −1  i  1 1 −i   1 −1  1 1   −i    1 1 i −1−1   −1    1 −i   −1 1 −i   1 −1 −1 −1    i −1 1 i −1 −1   −1    i −i   i 1 i 1  1 −1 i  i  −i 1 i −1 −1    i  i  i  i −1 i 1 −1  −i i −i    11 i −1 −1   −i  i 1  −i −1 i −1  1  i i 1  i 1 i 1  i i 1 1  −i −1 −i  1  i −i −1 1 −i   1 i 1  i i −1   1  1 −1 i 1  −i −1    −i 1 −1   1 i 1 i −i   1 −1   −1 −1 i 1  −i  i  i −1   1 1 i 1 −i 1   1 −1    1 1 −i  1  i  1 −1 −1   −1   1 i 1 −i 1   −i    i −1 1 i −1  i  1 −1 −1   1 1 i1 −i −1   −1   1 −1 1 −i   1  i −1    1 1 1 1 i 1 −i i 1 1  i −1 −i   1 −i −i −1 1  i 1 i 1 −i i −i   1 −1 −1 i 1  i −i  −i 1 1 1 i 1 −i −i   i −1    1 −1 i 1  i  i  i −1   −1   1 i −1  1 1   1 1  i 1 −i   −1 −1 1  −i 1 −i   1 i −1  1 1   −i    i  i 1 i 1 −1  1 −1 −i   −1   1 i −1 1 −1   −1   −1   −1 1 −i   −1 −1 −1    1 −1   1 1 i −1  1 i 1 −1   −1−1 −i   −1  1 −i −1 −1   −1   1 i −1  1 i −i    i  1 −1 i 1  1 −i −1 −i  1 1 i −1  1 −i    i 1  i −1 i −1 −1  i  1 1 −i   1 i −1 −1   1   1 1 −i 1 −i   −1  1  1 −1 1  i 1 i −1 −1   1   −i   −i    i 1 i 1  1  1  −i i −i   1 i −1 −1   −1   −1   1 −1 1 −i   1 −1 −1    1 −i   −1   1 i −1−1   i 1 −1    1 −1 −i   −1 −1 −i −1 −1   1 1 i −1 −1   i −i    i −1 −1i 1 −1 −i  −i −i   −1   1 i −1 −1   −i   −i   −1    −i −1 i −1  1  i  −i−1    i 1 i −1  i  1 1   1 −1 1 −i −1   −1    1 −1    1  1 1 i −1  i  1−i    i −1 1  i  1 −i    1 −i    −i  1 1 i −1  i −1 −1    i  i 1 −i  1 1−1 1 −1  i 1 i −1  i  i 1   −1    −i −1 −i −1   −1   −1 −1   −1  −i 1 i−1  i  i −i    i  i −1  i  1 −i    −i −i    −i  i 1 i −1  i  −i −i   −1  −1 −1  i −1   −i    i −i   −1  1 1 i −1 −i  1 −1   1 −1 1 −i −1   1  11  1  1 1 i −1 −i −1 1   −1    1 1 −i −1   −1   −1 −1   −1 −1 1 i −1 −i−1 i  i  1 1  i  1  i −1  i  −i −1 1 i −1 −i  i i  i  i −1  1  1  i  −i i  −i  i 1 i −1 −i  −i −1   1  −i −1 −i −1   1  i 1  1  −i 1 i −1 −i −i −i   −1    1 −1  i −1   −i    i −i   −1 −1 1 i  i  1  i −i   1 −1 1−i −i 1  1 1 −1 −1 1 i  i  1 −1 1   −1    1 1 −i −i −1   −1 −1    1  1 1i  i  1 −1 i 1  i 1  i −i  i −1  i −1  −i 1 i  i  1  i i 1 −1 −1  i −i i  −i  i −1 −1 1 i  i  1  −i i −i    i −1  i  i  i  i  i  −i  −i 1 i  i−1    1 −1   1  1 1 −i −i 1  1 1 −1  1 1 i  i −1   −1 1   −1   −1 1 −i−i −1   −1 −1    1 −1 1 i  i −1   −1 i 1  −i 1  1 −i 1 −1 1 −1  i 1 i  i−1    i i −i    i −1  i  i  i  −i  i  −i  −i 1 i  i −1    −i −i   −i   −i −1 −i  i 1  i 1  −i −1 1 i −1  i 1 −1   1 1 1 −i −1    −i  1  1 1 −11 i −1  i −1   1 −i    i 1 −i  1  i −1   −1    i  i 1 i −1  i −1   1 −i  1 1  i  1  −i −1    i  i −1 1 i −1  i  i  i  i −i   −1  i  1  i −i  i−i    −i 1 i −1  i −i   −1   −1   −i   −1 −i −1    i  i  1 −1    −i 1 i−1 −i 1 1 1 1 1 −i −1    i  1 −1   1 −1 1 i −1 −i 1 −i    i 1 1  i  1  i 1 −i −i   −1 1 i −1 −i −1   −1   −1   −1   1 −i −1    i −1    1 −1    11 i −1 −i  i 1 1 −i   −1 −i −1    −i −i −1   1  −i 1 i −1 −i  i −i    i−i   −1  i  1  −i −i −i −i    −i 1 i −1 −i −i    i 1 1 −1  i −1    i  i i 1 −1 1 i  i  1 1 1 −1   −1   1 −i −i  1  1 −1   1 −1 1 i  i  1 1 −i  1  i 1  i −i −1  1 −i −1   −1 1 i  i  1 −1   −1   1 1 1 −i −i  1 −1    1−1    1 1 i  i  1  i 1  i −1   −1 −i  i  1 −i −1    i −1 1 i  i  1 1 −i   i −i   −1  i  i −1 −i −i  i  i 1 i  i −1   1 1 −1   1 1 −i −i −1  1−1   1  1 1 i  i −1   1 −i   1 −i   1  i −i  1  1 −i −1    i 1 i  i −1  −1   −1   1 −1   1 −i −i −1 −1    1 −1   −1 1 i  i −1    i 1 −i   −1  −1 −i  i −1 −i −1   −i   −1 1 i  i −1    i −i   1 −1   −1  i −i −1 −i −i−1   −1 1 i  i −1   −i   −i   −1   −1   −1  i −i −1  i −i 1 −1 1 i i i 11 −1   −i   1 −i −i   i 1 −1 1   −1 1 i i i 1 −i   1   −1   1  1 −1   −i  1 −1 −1    1 1 i i i −1   −1   i 1 1 −i i −i   −1    1 i −1 1 i i i  i1 i −i   −1 −1   i i −i   −1 i  −i 1 i i i  i −i   1    i −1  i −i   i−i    −i −1    1 1 i i i −i    i −1   −i   −1  1 −1   1   1  i 1   −1 1i i −i   1 1 −1    i 1 −1   −1   −i   1 −1 1    i 1 i i −i   1 −i   1  1 1  i −i   i 1  −i −1   −1 1 i i −i   −1   1 i 1 1 −i i i −1   −1 i −11 i i −i    i 1 −i   −i   −1 −1   i −1   −i   −1 −i    −i 1 i i −i    i−i   i −1   −1  1 i 1   −i   −1 i  1 1 i i −i   −i    i −i   1 −1  i i i i  i −i   −1 1 i −i   1   1 1 i  i 1 −i −i   −1   1 −1 i  −i 1 1   −1  1   1 −i   −1    i 1  1 1   −1   1 −1 1   −1 1 i i  i  1 −1  1 −i 1 −i−i i  1 1 −1   −i 1 i i  1 −1  1 −1  1 1 −i −1   i −1 −1   1  1 1 i i  i−1  i −1  1 1  i −i −i   −1  i 1 −1   1 i i  i  i  i  1 −i −1  i −i i −i  i −1   −i 1 i i  i  −i −1  i −i −1 −i  i i  i 1  i −i 1 i i  i  −i −i −1  i −1  i −i i  i −i   1  i 1 i i −i  1 −1  1  i 1 −i −i −i    1 1−1    i 1 i i −i −1  1 −1 −i 1 −i −i −i   −1 −1   1 −i 1 i i −i −1  i  1 1 1  i −i i −1  i −1   −1   1 i i −i  i  i  −i −1   −1  i  i i  −i  i−i    1 1 i i −i  −i −1  −i −i −1 −i  i −i    i 1 −i   −i 1 i i −i  −i −i  i  1 −1  i  i i  i −i    i −1   1 i −i    1  1 −1  i −i 1 −i −i −1   1 1  i  i 1 i −i    1 −1 −1 −1  1 1 −i  i 1   −1 1 1  1 1 i −i 1 −1   i  1 −i   1  i  i −1 −1    i −1    i 1 i −i 1  i  i  i −i   −1  i −i −1−i  i  i  i 1 i −i 1 −1   −1   −i −1   −1 −i −1    1  1  1 −i −1   1 i−i 1 −i   −i −i i −1  i −i −1  i −i −i −i 1 i −i −1   1 −i  i i 1 −i −i 1  1  1  i −i 1 i −i −1   −1    1  1 −1   1 −i  i −1 −1   −1   −1   −i1 i −i −1   −1    i  1 i 1  i  1  1 −1    i −1   −i 1 i −i −1    i  i  ii −1  i −1    1 −i  i  i −i 1 i −i −1   −i    i  i −i   −1  i −i  1  i i  i  i 1 i −i  i 1  1  1 −i   1 −i  i  i  1 −1   −1   −i 1 i −i  i 1−i −1   −1   1  i  i  −i  1 −i  1  1 1 i −i  i −1   −1   −i 1   1 −i −i −i −1    1 −i −1   1 i −i  i 1  1 −i −i   −1 −i −i  1 −i −1   −i −i 1 i−i  i  i −i −i 1   −1  i −i  −i −i −i −i −1   1 i −i  i −i   −i  1 i −1 i  i  i  i −i −1    i 1 i −i −i   1 −1   −1   i 1 −i  i  −i  1  1  1  i1 i −i −i   −1   −1   −1   −i   1 −i  i −1 −1    1  1 −i 1 i −i −i    i 1 −i i −1 −i −1    −i −i −1   −i  i 1 i −i −i    i −i −i −1   −1  i −i i −i −i −i  1 1 i −i −i   −i    i  i 1   −1  i −i  i  i  i  i −1   1 −i   1 1 1  1 −i −1   1  i −1    1  1 −1    i −1   1 −i    1 1 1  i −i i 1−i −1   −1  1  i  i −i 1 −i    1 1 −1   −i −i i 1 −i −1   −1 −1   −i  1−i 1 −i    1 1  i −i −1   −i   −1 −i  1 −1 −i −i −1    i 1 i −i 1  i 1−i −1 −1 −i   −i 1  −i −1   −i −1 1 i −i 1  i −i   −i −1 −1 i −i −1   −1−i   −i  i 1 i −i 1 −i 1  i  1 −1 i −i −1    1 1  i −1 1 i −i −1    1 1 i  −i 1 −i   −i 1  1 −1    i  i 1 i −i −1    1 −i    1  i 1 i  i 1  1−i   −1    −i 1 i −i −1   −1   −1   −1   −1 1 i  i −1   −1 1  1 −1 1 i−i −1    i 1  i −1 −1 −i   −i −1   −1 −1    i −1 1 i −i −1    i −i   −i i −1 i −i 1  −i −i   −i  −i 1 i −i −1   −i −i    1 −1 −1 i  i 1  i −i  −1   −1 1 i −i  i  1 −1    i  1 1 −i   −i −i    1 1  i −1 1 i −i  i −1  1 −i −1 1 −i   −i −i   −1 −1   −i  1 1 i −i  i −1    i −1   −1 1 1    1−i   −1 1  1  1 1 i −i  i  i  i  i  1 −1 1   −i −i    −i 1  1 −1 1 i −i i −i −1   −i  −i −1 −i   −i  i  i 1 −i  −i 1 i −i −i    1 1  1  i 1 −i   i −i    1 −1   −1    i 1 i −i −i   −1   1  1  −i 1 −i    i −i   −1 −1  −1    −i 1 i −i −i   −1    i −1    1 1 i  i  i −1 1  1 −1 1 i −i −i   1  i  i −1 −1 i −i  i  −i 1  i  1 1 i −i −i   −i −1   −i  i −1 −i   −i−i    i 1 −i  i 1 i −i −i   −i −i   −i  1 −1 i −i  i  i −i   −i −1 1 −i   1 1  1 −1    i −1 1 i −1   1  1 1 −i −1 1 −i    1 1 −1   1 −i  1 1 i−1   1 −1 −1    1  1 1 −i    1 1  i −1   −1    1 −1 i  1 1  −i 1 −1    11 −i    1 1 −i 1  1 −1 −1 i  1 1  i −1   −1   −1 1 −i 1 1 −i    i 1 i −1−i 1  i i  i 1 −i   1 −i 1 −1   1 −1   −1   −i   1  i 1 1 1   1 −1   i 1−i 1 −1   1  i −i   −i   1 −i −1 1 i  i  i 1   1 −i 1 −1   −1   −1    i−1   1  i −1 −1   1   1 −i   −1   1 −i 1 −1    i  i 1 i −1 −i 1 −i   i i 1 −i   1 −i 1 −1   −i    i 1 −i   −1 −i 1  i i  i 1 i 1 −i 1  i 1  1−1   1   1  i 1 1 −1   −1   −1   −1   1 −i 1  i 1  i  i 1   1 −i −1 1 i i −i   −1   1 −i 1  i −1    1 −i   i 1  i −1 −1   −1   −1    i i 1 −i 1 i −1   −i  i 1   1 −i −1 −1   −i   −i   −i   −1   1 −i 1  i  i −1   −1  i −1  i 1 −i   1   1 −1   i 1 −i 1  i  i −i −i   −i   −1 −i −1 −i   −i  −i    i −i   1 −i 1  i −i   −i −1   −1   −1 −i 1  i −i   −i   −1   1  1 −i 1 −i   1 −1    i i 1  i −1 1 1   1 −i   i 1 −i 1 −i   −1    1 −1  −1   1  1 −1 −1   −1   −1    i −i   1 −i 1 −i    i −1   1 i −1  i 1 −i  1   1 1 i 1 −i 1 −i    i −i −i   i −1 −i −1 −i   −i   −i    i i 1 −i 1−1   −i    i 1 1   −1 −i 1  i i  i 1 −1   1 −i −1   1 1  1 1 −i   1  i−1 1 −1   −1   1 i 1 −i −1   1 1  1 1 i 1 −i 1 1 i  i −i   −i   1 −i −1  1 −1   −1   −1   i 1  1 −1 −1   1   1 −1   −i   1 −i −1   1 −1   −i −i  −i   1 −i 1 −1   −i   −i    i i 1 −i −1   1  i −i 1 −i   −1 −i −1 −i  −i   −i   1 i 1 −i −1   1 −i   −i 1 i −1 −i −1  i i −i   1 −i   1 −i −1  −1   1 −1   −i   1   1  i 1 1 1   1  i 1   1 −i 1  1 −i   −i    i −1  −1 −i   −1 1  i  −i  −i −1   1 −i 1 −1 1  i  i i 1 −i   −1 1  1  i  −i−i   1 −i 1 −1 −1   1  −i −1   1 i −1 −1   −1 −1  i −1   1 −i 1 −1 −1  −i    −i −i   1 −i   −1 1 −1  −i  i i 1 −i 1 −1  i −i   −1 i −1 −i   1 1 −i  −i −1 −i   1 −i 1 −1 −1   −i   −1 −1   −1 −i   1 1  i  −i −1 i 1 −i1  i 1 −1   −1 −1   1 i 1 −i    1  1 −1 1   1 −i 1  i −1   1  1 1   1 i1 −i   −1 −1  1 −1   1 −i 1  i −1   −1    i i 1 i −1  i −1  1  −i i 1 −i1  i  i −1    1 −i   −1 i 1  i −1  1  1 −i   1 −i 1  i  i 1 −1 1   −1 −i  −1 1 −1  1  i i 1 −i 1  i −i   1 −1 i −1 i 1  i  i −1 −1 i 1 −i 1  −i1 1  −i i 1 i −1 −i    1 −1  i i 1 −i 1  −i 1  i  −i 1   1 −i   −1  i  1 1  i −1   1 −i 1  −i −1   −1    1 1   1 i 1 1 −1  1  1 −1   1 −i 1  −i1 1  −i −1   −1 −i   −1 −1   −1  i  1 −i   1 −i 1  −i −i   1  1 i −1 i 1−i    i −1  1 i 1 −i 1  −i −i   −i   −1 1   −1 −i   1  i  i  −i −1 −1  1 −i −1  1 1 −1    1 i 1 i −1 −1    1  1  1 −i   1 −i −1  1 −1   1 −1 −i  1 i −1 −1   −1 −1 −1 i 1 −i −1  1 −i   −i    i i 1 −i   1 −1   −1 −1 −i −i   1 −i −1  1  i  i −1 −i   −1 −i   −1 −1    −i  i −1 i 1 −i −1  1−i   1 −1 −1   −1 i −1 1  i −1 −1 −1   1 −i −1 −1 1 1  1 i 1 i −1 1  1−1  1 −i   1 −i −1 −1 1  i  −i i 1 −i   1 1  1  1  i −i   1 −i −1 −1 −1  1  i −1 1  i  1 −1 −1   −1    −i −1 1 −i −1 −1 −1   −i   −i    i 1 −i 1  1 −1   −i    i  −i 1 −i −1 −1 1 1 1 −1 −1 −i  1 −1 −1   1  −i −1 1−i −1 −1 −1   1 −1   −1 −1 −i  1 −1 1 1  1 −1 1 −i −1  i 1 1  i −1 1  i 1  i 1 −1    −i  −i 1 −i −1  i −1   1 −1    1 1  i −1  −i −1   −1   −1−1 1 −i −1  i −1   −1   −i    1 1 −i  1 −1 −1   −1    i −1 1 −i −1  i  i i  i  i −1 −i  1  i −i   1  −i  i 1 −i −1  i −i   1 −1    −i −1  i −1 i  i −1   −1  −i 1 −i −1  i −i   −i   1 −1 −1 −i −1  −i  i −1    1  1 1−i −1  −i 1 −1   1  1 1  i −1  i 1 1  1 −1 1 −i −1  −i −1   −1   −1    11  i −1  i −1   1 −1 −1 1 −i −1  −i  i −1   −1    1 −1  i −1  −i −i   1−1  i 1 −i −1  −i  i −i   1 −1 −1 −i −1  i −i   −1    1  1 1 −i −1  −i−i    i −1    1 −1 −i −1  i  i 1 −1 −1 1 −i  i  1 1 1 1 −1 1  i −1  1 1−1   −1 −1 1 −i  i  1 1  i 1  i 1 −i −1 −1 1 1 −1  −i 1 −i  i  1 −1   −1   i  i 1  i  i −1 −1   1  i  −i 1 −i  i  1  i −1    i −1 −1  i  i  1 −i  1  i −1 1 −i  i  1  i −i   1 −1 −1 −i  −i  1 −i   −1   −1 −1 1 −i  i 1 −i    i  i  i −1 −i  i −1  i  i  i  −i 1 −i  i −1 1 1 −1    1 1  i  1 1 1 −1    −i  −i 1 −i  i −1 1  i 1  −i 1 −i −1  1 1  i −1  i 1 −i  i −1−1   −1   −1   −1 1  i  −i −1 −1   1  1 −1 1 −i  i −1  i −1    i  1 −1 i  i −1 −i   1  1  1 1 −i  i −1  i −i   1  1 −1 −i  −i −1 −i   −i   −1 1 1 −i  i −1 −i    i  i  −i −1 −i  i  1  i  i  i  i 1 −i  i  i 1 1 1 −i 1  i −1  1 1 −1   −1  −i 1 −i  i  i 1  i 1 −1 1 −1    −i −1 1  i −1 1 1 −i −1 −1 −1   −1 −i    −i 1 i 1 −1 −i    1  i −1 1 −i −1 −1  i −1−1    1 −1 i −1   −1 −i    1 −1  1 1 −i −1 −1 −i  1 −1    1 −1 i −1   −1 i −1   −1  1 1 −i −1 −1 −i −1 −i    1 −1 −i   1 −1  i −i  i  1 1 −i −1 i  1 −1 −i    −i 1 i 1  i 1  1  i  −i 1 −i −1  i −1   −1 −i    i 1 i 1 i −1    1  i  1 1 −i −1  i  i −1 −1    −i −1 i −1    i −1    1 −1  −i 1−i −1  i  i −1 1 −1 −1 −i   1  i −1   −i −1  −i 1 −i −1  i −i  i −i    i−1 −i   1  i  i  i  i  i 1 −i −1  −i  1  1 1 −1 1 i −1    i  i −1    1 1 1 −i −1  −i  1  i  i  1 1 −i   1  i 1  i  −i −1 1 −i −1  −i −1    −i i  1 1 −i   1  i −1   −i  −i −1 1 −i −1  −i  i  i  i  −i −1 −i   1  −i−i    i  −i  −i 1 −i −1  −i −i  1 1  −i −1 i −1    −i 1 −1    1  −i 1 −i−1  −i −i  −i 1  1 −1 −i   −1    i  i −i  1 −1 1 −i  i  1  1 −1 −1   −11 i −i    1 1  1  1 −1 1 −i  i  1 −1    1  i  −i 1 i  i −1 −1   −1    i −i 1 −i  i  1 −1    −i 1  i 1 −i   −i   −1 −1   −i −1  −i 1 −i  i  1  i i 1  −i −1 −i    i −1 −i    i  i  i 1 −i  i  1 −i  1  i −1 −1 i  i  1 i −1    i −1 1 −i  i  1 −i  −i −1   −1 −1 −i   −i    1  i −i  i −1 1 −i i −1  1 −1 −i   −1 1 i 1  1 1  1  −i  1 1 −i  i −1 −1    1 1 −1 1 i −1  −1 −1   −1   −1 −1 1 −i  i −1 −1   −1 1  −i 1 −1   −i    1 −1   −i −1 i 1 −i  i −1  i  i 1 −1 −1 −1   −i   −1 −i    i −1 −1 1 −i  i −1 −i  1−i   −1 −1 i  i −1  i −1    −i −1 1 −i  i −1 −1    −i −i   −1 −1 −i    i 1 1 −i −1  i 1 −i  i  i  1 −1 −1   −1 1 i −i    i 1  1  1 −1 1 −i  i  i 1  i −1    1 1 −i   −i    −i 1  i  1 −1 1 −i  i  i −1    1 i  1 1 i i−i   −1   −1   i −1 1 −i  i  i i −1 −i    i −1 i i i −i 1 −i    i 1 −i i  i i  −i −i    1 −1 −i   i −i   −i −i   −i   −1 1 −i  i  i −i    −i−1    −i −1 −i   −i   i  i −i   1    −i 1 −i  i −i   1   −1 −i    1 1 ii i  1 1 −i   −1 1 −i  i −i   −1    1 i −1 1 i i i −1   −i   i  1 1 −i i −i   −1    −i −1   −1 1 −i   −i   i −1   −i   1    1 1 −i  i −i   i i i −1 −1 −i   i i −i  i i  1 1 −i  i −i   −i    i i  1 −1 −i   i i  i i i −1 1 −i −i 1 1    1 i  −i 1 i −i   −1    1 −1   i  i 1 −i −i 1 1   i −1    i 1 −i   i −1    1  i 1    −i 1 −i −i 1 −1   −1 1    1 1 i i 1  −1   1 −1    1 1 −i −i 1 i −1 i  1 −1 i −i   1   −1   1 i  1 1 −i −i 1i  −i −1   −1 −1 −i   i 1   −i −i   1   −1 1 −i −i 1 −i    i −i    i −1−i   −i   −1    i  i −i    −i 1 −i −i −1   1    1 i  i 1 i −i   1    1−1   i  −i 1 −i −i −1   1    i 1    i 1 −i   i 1    1  i −1    −i 1 −i−i −1   −1   −1 1   −1 1 i i −1   −1   1 −1   −1 1 −i −i −1   i −1 i −1−1 i −i   −1   −i 1 i −1 1 −i −i −1   i  i −i    i −1 −1   −i   1   −i i −i    −i 1 −i −i −1   −i    1 i −1 −1 i −i   −1    i −1   i −1 1 −i i  i −1 −i   −1 1 1 −i −i    −i −1 −i 1   −1   1 −i  i  i  i 1  i 1 −1−i 1   −1  −i  i 1   −1   1 −i  i  i  −i 1  −i  i −1  i i  i  i −1   −1   i 1 −i  i −i  1 1  1  i 1  i −1   −1  1 −1   −1    i 1 −i  i −i  1  i−1 −1   1 −i −i    i  1  i 1    1 1 −i  i −i −1 −1    i 1 1  i i  i −1 1 i −1   1 −i  i −i  1 −1    −i −i   −1  i i −1  −i  1 −i   −i 1 −i  i−i  −i 1  −i −i   −1  i i  −i  i −1   −i   −i 1 −i  i −i −1 −1   −1 1 −1−i 1    i  i −i −i   −1   1 −i −i  1  1 −1    i  i 1  i −i   −1  1  1 i−i 1 −i −i  1 −1 1  −i −i   1  i −i   −1 −1 −1   −i    i 1 −i −i  1 −1−i    1 −i   1 −i i −1 −1 −i −1    i 1 −i −i  1  i  i −1 1 −1 −i i  1 −i  i 1    1 1 −i −i  1  −i 1  1 1 −1  i −i    1  i −1   i  1 1 −i −i 1  −i −i    i  i −1 −i −i   −1  i −i i −i 1 −i −i −1    1 −1    1 1 1 i i −1  1  1 −1    1 1 −i −i −1   −1 1 −1 −1   1  i i −1 −1 −1   i −1  1 −i −i −1   −1 −1    1  i 1 −i i  1 −1 −i −1   −i 1 −i −i −1    i  i −1−1   −1 −i i −1  −i  i 1   −1   1 −i −i −1    i −1    i  i −1 −i −i    1 −i −i i −i 1 −i −i −1   −1 1  −i −i   −1 −1   −i    1  i  1 −i    i 1−i −i −1    −i −i    i −i −1 −i −1   1    i  −i  i  i 1 −i −i  i  1 −1   1 −i 1  i  i i  1  1 −1   −i 1 −i −i  i −1 1 −1    i 1  i  1 i −1 −1 1 i 1 −i −i  i −1 −i   −1   −1   1 −i  1 −i   −1  −i 1  1 1 −i −i  i  i i −i  1 −1 −i −i −i    −i  i −i   −1   1 −i −i  i  −i 1 −i −i −1  i −ii  i −1 −i   −i 1 −i −i −i  1 1  i −1   1  i −i i  1 −1  i  1 1 −i −i −i−1 1 −1   −i 1  i  i −i   −1 −1 1 −i 1 −i −i −i −1 −1   −i  1 1  i −1  i −1  1 −i   −1   1 −i −i −i  i  i −1   −i −1 −i  1 −i    −i  i 1 −i 1−i −i −i  i −i    i −1   −1 −i −i i  −i  −i  i  1 1 −i −i −i  −i  i −i 1 −1 −i −i i  i  i −i   −1   1 −i −i  i 1  1 −1   −i   1 1    1  i  1−1    1  −i 1 −i −i  i 1  i 1 1 1 −i    i −i  1  i −1 −1 1 −i −i  i −1  −1 1  i 1 i  i  i −1   1 −1  i 1 −i −i  i  i −1 −i   −i   −1 i −i  i −i1  −i  −i 1 −i −i  i  i  −i  i 1 −1 −i   −i −i −i −i    i −1 1 −i −i  i−i   −1 1 −1   −1 −1    i  1  i −i   −1 −1 1 −i −i −i 1 −1  i 1 1 i −i i  1 1  i −1 1 −i −i −i −1   −1 1 −i   1 i  i −i −1   1 −1  −i 1 −i −i−i  i −1  i −i   −1 i −i −i −i 1  i  −i 1 −i −i −i 1  −i −1    i −1 −i   i −i −i −i    1  i 1 −i −i −i −i    1 −i    i −1 i −i −i  i −1    −i  i1 −i −i −i −i    −i  i 1 −1 −i   −i  i  i −i    i −1

Among the total 6144 phase rotation factor sequences, the remaining 5440sequences except the 704 baseline sequences shown in Table 9 can beestimated from the 704 baseline sequences according to the followingmethods. Hereinafter, examples of obtaining the remaining sequences fromthe baseline sequences will be explained. In Equations 16 to 18, γ_(k,l)indicates a baseline sequence and k and l denotes a row and column ofthe corresponding baseline sequence in Table 9, respectively (where1≤k≤352, l={1, 2}). For example, if k and l is respectively equal to 3and 2 (i.e., k=3 and l=2), it indicates the baseline sequence shown inthe third row and the right column of Table 9. In addition, χ_(k,l)indicates a sequence derived from the baseline sequence based onEquations 16 to 18.

As a first embodiment, it is possible to consider a case where thebaseline sequence is multiplied by a prescribed constant α as shown inEquation 16.

Equation 16χ_(k,l)=αγ_(k,l)  [Equation 16]

In Equation 16, α may be {1,−1, i, −i}.

As a second embodiment, a sequence can be generated by cyclic-shiftingthe baseline sequence as shown in Equation 17.

Equation 17χ_(k,l)=γ_(k,l) ^((m))  [Equation 17]

In Equation 17, m denotes a cyclic shift value.

As a third embodiment, a sequence can be generated by arranging thebaseline sequence in reverse order as shown in Equation 18.

Equation 18χ_(k,l)=rev(γ_(k,l))   [Equation 18]

In Equation 18, rev(.) indicates an operation of arranging a specificsequence in reverse order. For example, a result of rev([1 2 3]) becomes[3 2 1] (i.e., rev([1 2 3])=[3 2 1]).

Additionally, a new sequence can be generated by simultaneously applyingat least two embodiments among the embodiments proposed in Equations 16to 18.

FIG. 18 is a flowchart illustrating a method for generating a sequenceaccording to proposed embodiments. Specifically, FIG. 18 shows a timeseries flow of the aforementioned embodiments. Thus, it is apparent thatalthough the aforementioned features are not explicitly shown anddescribed in FIG. 18, the features can be applied in the same or similarmanner. Meanwhile, although in FIG. 18, an embodiment is describedfocusing on AP operation, a sequence for a UE can be generated in thesame manner.

First, an AP generates a basic sequence structure [S1810]. Here, thebasic sequence structure means a series of values repeatedly used forgenerating sequences for 20, 40, and 80 MHz bandwidths. For instance,the basic sequence structure may mean 244 tones (i.e., C₅₂ 0₁₂ C₅₂ 0₁₂C₅₂ 0₁₂ C₅₂) obtained by eliminating the first component 0₅ and the lastcomponent 0₇ from the sequence for the 20 MHz bandwidth in Equation 2.

After generating the basic sequence structure, the AP substitutes 0₁₂ ofthe basic sequence structure with D₁₂ [S1820]. In this case, D12 can bedefined as shown in Equation 5. Alternatively, unlike Equation 5, it canbe defined such that non-zero values are repeated at an interval of 2tones. Hereinafter, the structure obtained by applying D₁₂ to the basicsequence structure is referred to as a substituted structure or a D₁₂sequence structure.

Thereafter, the AP selects a phase rotation factor used for generating asequence [S1830]. A plurality of phase rotation factors for an optimalor suboptimal PAPR can be determined in each bandwidth in advance andthe UE selects any one from among the plurality of the phase rotationfactors. Meanwhile, the phase rotation factor γ_(k) may includedifferent numbers of components depending on bandwidths.

The AP generates a final sequence for a corresponding bandwidth usingthe D₁₂ sequence structure and the phase rotation factor [S1840]. Thisstep may be performed by applying the phase rotation factor in the unitof {C₁₂D₁₂} or {C₁₂} as described above. That is, in the 20 MHzbandwidth, the final sequence is generated by applying the phaserotation factor as shown in Equation 8.

Meanwhile, although the sequence generation procedure is described withreference to the 20 MHz bandwidth, the steps S1830 and S1840 may bechanged in 40 and 80 MHz bandwidths. As described with reference toEquations 9 and 10, a sequence for the 40 MHz bandwidth is generated byrepeating a sequence obtained by eliminating some components (the first0₅ component and the last 0₇ component) from the sequence of the 20 MHzbandwidth and a sequence for the 80 MHz bandwidth is generated byrepeating a sequence obtained by eliminating some components (the first0₅ component and the last 0₇ component) from the sequence of the 40 MHzbandwidth.

In this case, the phase rotation factor is defined to have twocomponents for the 40 and 80 MHz bandwidths, respectively. The UE mayselect any one from among a plurality of predetermined sequences.

Alternatively, phase rotation factors for the 40 and 80 MHz bandwidthsmay be determined by the unit of {C₁₂D₁₂} or {C₁₂} as described withreference to Equations 11, 12, 13, and 14. In this case, a phaserotation factor may include 8 or 16 components and the AP generates asequence by selecting any one from among a plurality of predeterminedsequences.

According to another embodiment, a sequence derived from a baselinesequence according to the embodiments described with reference toEquations 166 to 18 can be used as a phase rotation factor.

After generating a sequence according to one of the proposedembodiments, the AP transmits the corresponding sequence to the UE. Thatis, the generated sequence is inserted into a preamble of a frame fortransmission thereof. In addition, the sequence is utilized forsynchronization between an AP and a UE, channel measurement, AGC, etc.Moreover, it is apparent that the embodiments described in FIG. 18 canbe applied to a UE in the same or similar manner.

4. Apparatus Configuration

FIG. 19 is a block diagram showing the configuration of a user equipmentand a base station (or, AP (Access Point)) according to one embodimentof the present invention. In FIG. 19, the user equipment 100 and thebase station 200 may include radio frequency (RF) units 110 and 210,processors 120 and 220 and memories 130 and 230, respectively. Althougha 1:1 communication environment between the user equipment 100 and thebase station 200 is shown in FIG. 19, a communication environment may beestablished between a plurality of reception module and the transmissionmodule. In addition, the base station 200 shown in FIG. 19 is applicableto a macro cell base station and a small cell base station.

The RF units 110 and 210 may include transmitters 112 and 212 andreceivers 114 and 214, respectively. The transmitter 112 and thereceiver 114 of the user equipment 100 are configured to transmit andreceive signals to and from the base station 200 and other receptionmodules and the processor 120 is functionally connected to thetransmitter 112 and the receiver 114 to control a process of, at thetransmitter 112 and the receiver 114, transmitting and receiving signalsto and from other apparatuses. The processor 120 processes a signal tobe transmitted, sends the processed signal to the transmitter 112 andprocesses a signal received by the receiver 114.

If necessary, the processor 120 may store information included in anexchanged message in the memory 130. By this structure, the userequipment 100 may perform the methods of the various embodiments of thepresent invention.

The transmitter 212 and the receiver 214 of the base station 200 areconfigured to transmit and receive signals to and from anothertransmission module and reception modules and the processor 220 arefunctionally connected to the transmitter 212 and the receiver 214 tocontrol a process of, at the transmitter 212 and the receiver 214,transmitting and receiving signals to and from other apparatuses. Theprocessor 220 processes a signal to be transmitted, sends the processedsignal to the transmitter 212 and processes a signal received by thereceiver 214. If necessary, the processor 220 may store informationincluded in an exchanged message in the memory 230. By this structure.the base station 200 may perform the methods of the various embodimentsof the present invention.

The processors 120 and 220 of the user equipment 100 and the basestation 200 instruct (for example, control, adjust, or manage) theoperations of the user equipment 100 and the base station 200,respectively. The processors 120 and 220 may be connected to thememories 130 and 230 for storing program code and data, respectively.The memories 130 and 230 are respectively connected to the processors120 and 220 so as to store operating systems, applications and generalfiles.

The processors 120 and 220 of the present invention may be calledcontrollers, microcontrollers, microprocessors, microcomputers, etc. Theprocessors 120 and 220 may be implemented by hardware, firmware,software, or a combination thereof.

If the embodiments of the present invention are implemented by hardware,Application Specific Integrated Circuits (ASICs), Digital SignalProcessors (DSPs), Digital Signal Processing Devices (DSPDs),Programmable Logic Devices (PLDs), Field Programmable Gate Arrays(FPGAs), etc. may be included in the processors 120 and 220.

Meanwhile, the aforementioned method may be implemented as programsexecutable in computers and executed in general computers that operatethe programs using computer readable media. In addition, data used inthe aforementioned method may be recorded in computer readable recordingmedia through various means. It should be understood that programstorage devices that can be used to describe storage devices includingcomputer code executable to perform various methods of the presentinvention do not include temporary objects such as carrier waves orsignals. The computer readable media include storage media such asmagnetic recording media (e.g. ROM, floppy disk and hard disk) andoptical reading media (e.g. CD-ROM and DVD).

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the inventions. Thus, itis intended that the present invention covers the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

INDUSTRIAL APPLICABILITY

Although a sequence generation method is mainly described based on anIEEE 802.11 system and an HEW system, the method can be applied tovarious kinds of wireless communication systems as well as the IEEE802.11 system and the HEW system.

What is claimed is:
 1. A method of transmitting a preamble comprising a sequence, the method performed by an access point (AP) in a wireless local area network (WLAN) system and comprising: generating, by the AP, a basic sequence structure including one or more C₅₂s and one or more D₁₂s, wherein each of the one or more C₅₂s is composed of 52 tones, and wherein each of the one or more D₁₂s is composed of 12 tones and has a non-zero value at an interval of 4 tones; selecting, by the AP, one phase rotation factor from among a plurality of phase rotation factors predetermined for bandwidths for communication with a user equipment (UE); generating, by the AP, the sequence based on the basic sequence structure and the selected phase rotation factor, wherein the selected phase rotation factor is applied to the basic sequence structure in a unit of a C₅₂ or a C₅₂D₁₂; and transmitting, by the AP, the preamble comprising the generated sequence to the UE.
 2. The method of claim 1, wherein the basic sequence structure is configured in the form of a C52D12C52D12C52D12C52.
 3. The method of claim 2, wherein the selected phase rotation factor is applied in the unit of the C₅₂D₁₂ to change a phase of each C₅₂D₁₂ of the basic sequence structure, and wherein the phase rotation factor is only applied in the unit of the C₅₂ to change a phase of the last C₅₂.
 4. The method of claim 1, wherein the D₁₂ is {0, 0, 0, 1+j, 0, 0, 0, −1−j, 0, 0, 0, −1−j}.
 5. The method of claim 1, wherein the sequence is generated by adding a 0₅ composed of five consecutive 0s to front of the basic sequence structure and adding a 0₇ composed of seven consecutive 0s, to back of the basic sequence structure.
 6. The method of claim 5, wherein, in a case of a 20 MHz bandwidth, the sequence comprising the 0₅ and the 0₇ is used without any change, wherein, in a case of a 40 MHz bandwidth, a sequence composed of two first partial sequences having a sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 20 MHz bandwidth, one D₁₂, one 0₅, and one 0₇ is used, and wherein, in a case of a 80 MHz bandwidth, a sequence composed of two second partial sequences having sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 40 MHz bandwidth, one D₁₂, one 0₅, and one 0₇ is used.
 7. The method of claim 6, wherein, in the case of the 40 MHz bandwidth, the phase rotation factor changes phases in a unit of the first partial sequence having the sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 20 MHz bandwidth, and wherein, in the case of the 80 MHz bandwidth, the phase rotation factor changes phases in a unit of the second partial sequence having the sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 40 MHz bandwidth.
 8. The method of claim 1, wherein the plurality of the phase rotation factors are generated by multiplying any single phase rotation factor by 1, −1, i, or −i, cyclic-shifting the any single phase rotation factor, or arranging the any single phase rotation in reverse order.
 9. An access point (AP) for transmitting a preamble comprising sequence in a wireless local area network (WLAN) system, the AP comprising: a transmitter; a receiver; a processor connected to the transmitter and the receiver and configured to generate the sequence, wherein the processor is configured to: generate a basic sequence structure including one or more C₅₂s and one or more D₁₂s, wherein each of the one or more C₅₂s is composed of 52 tones, and wherein each of the one or more D₁₂s is composed of 12 tones and has a non-zero value at an interval of 4 tones; select one phase rotation factor from among a plurality of phase rotation factors predetermined for bandwidths for communication with a user equipment (UE); generate the sequence based on the basic sequence structure and the selected phase rotation factor, wherein the selected phase rotation factor is applied to the basic sequence structure in a unit of a C₅₂ or a C₅₂D₁₂; and transmit the preamble comprising the generated sequence to the UE.
 10. The AP of claim 9, wherein the basic sequence structure is configured in the form of a C₅₂D₁₂C₅₂D₁₂C₅₂D₁₂C₅₂.
 11. The AP of claim 10, wherein the selected phase rotation factor is applied in the unit of the C₅₂D₁₂ to change a phase of each C₅₂D₁₂ of the basic sequence structure, and wherein the phase rotation factor is only applied in the unit of the C₅₂ to change a phase of the last C₅₂.
 12. The AP of claim 9, wherein the D₁₂ is {0, 0, 0, 1×j, 0, 0, 0, −1 −j, 0, 0, 0, −1 −j}.
 13. The AP of claim 9, wherein the sequence is generated by adding a 0₅ composed of five consecutive 0s to front of the basic sequence structure and adding a 0₇ composed of seven consecutive 0s to back of the basic sequence structure.
 14. The AP of claim 13, wherein, in a case of a 20 MHz bandwidth, the sequence comprising the 0₅ and the 0₇ is used without any change, wherein, a case of a 40 MHz bandwidth, a sequence composed of two first partial sequences having a sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 20 MHz bandwidth, one D12, one 0₅, and one 0₇ is used, and wherein, in a case of a 80 MHz bandwidth, a sequence composed of two second partial sequences having sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 40 MHz bandwidth, one D₁₂, one 0₅, and one 0₇ is used.
 15. The AP of claim 14, wherein, in the case of the 40 MHz bandwidth, the phase rotation factor changes phases in a unit of the first partial sequence having the sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 20 MHz bandwidth, and wherein, in the case of the 80 MHz bandwidth, the phase rotation factor changes phases in a unit of the second partial sequence having the sequence structure that the 0₅ and the 0₇ are eliminated from the sequence for the 40 MHz bandwidth.
 16. The AP of claim 9, wherein the plurality of the phase rotation factors are generated by multiplying any single phase rotation factor by 1, −1, i, or −i, cyclic-shifting the any single phase rotation factor, or arranging the any single phase rotation in reverse order. 